This problem is split into two tasks. In this task, you are required to find the minimum possible answer. In the task Village (Maximum) you are required to find the maximum possible answer. Each task is worth $$$50$$$ points.There are $$$N$$$ houses in a certain village. A single villager lives in each of the houses. The houses are connected by roads. Each road connects two houses and is exactly $$$1$$$ kilometer long. From each house it is possible to reach any other using one or several consecutive roads. In total there are $$$N-1$$$ roads in the village.One day all villagers decided to move to different houses — that is, after moving each house should again have a single villager living in it, but no villager should be living in the same house as before. We would like to know the smallest possible total length in kilometers of the shortest paths between the old and the new houses for all villagers. Example village with seven houses For example, if there are seven houses connected by roads as shown on the figure, the smallest total length is $$$8$$$ km (this can be achieved by moving $$$1 \to 6$$$, $$$2 \to 4$$$, $$$3 \to 1$$$, $$$4 \to 2$$$, $$$5 \to 7$$$, $$$6 \to 3$$$, $$$7 \to 5$$$).Write a program that finds the smallest total length of the shortest paths in kilometers and an example assignment of the new houses to the villagers.

The first line contains an integer $$$N$$$ ($$$1 < N \le 10^5$$$). Houses are numbered by consecutive integers $$$1, 2, \ldots, N$$$. Then $$$N-1$$$ lines follow that describe the roads. Each line contains two integers $$$a$$$ and $$$b$$$ ($$$1 \le a, b \le N$$$, $$$a \neq b$$$) denoting that there is a road connecting houses $$$a$$$ and $$$b$$$.

In the first line output the smallest total length of the shortest paths in kilometers. In the second line describe one valid assignment of the new houses with the smallest total length: $$$N$$$ space-separated distinct integers $$$v_1, v_2, \ldots, v_N$$$. For each $$$i$$$, $$$v_i$$$ is the house number where the villager from the house $$$i$$$ should move ($$$v_i \neq i$$$). If there are several valid assignments, output any of those.


The king's birthday dinner was attended by $$$k$$$ guests. The dinner was quite a success: every person has eaten several dishes (though the number of dishes was the same for every person) and every dish was served alongside with a new set of kitchen utensils.All types of utensils in the kingdom are numbered from $$$1$$$ to $$$100$$$. It is known that every set of utensils is the same and consist of different types of utensils, although every particular type may appear in the set at most once. For example, a valid set of utensils can be composed of one fork, one spoon and one knife.After the dinner was over and the guests were dismissed, the king wondered what minimum possible number of utensils could be stolen. Unfortunately, the king has forgotten how many dishes have been served for every guest but he knows the list of all the utensils left after the dinner. Your task is to find the minimum possible number of stolen utensils.

The first line contains two integer numbers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 100, 1 \le k \le 100$$$)  — the number of kitchen utensils remaining after the dinner and the number of guests correspondingly. The next line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 100$$$)  — the types of the utensils remaining. Equal values stand for identical utensils while different values stand for different utensils.

Output a single value — the minimum number of utensils that could be stolen by the guests.

NoteIn the first example it is clear that at least one utensil of type $$$3$$$ has been stolen, since there are two guests and only one such utensil. But it is also possible that every person received only one dish and there were only six utensils in total, when every person got a set $$$(1, 2, 3)$$$ of utensils. Therefore, the answer is $$$1$$$.One can show that in the second example at least $$$2$$$ dishes should have been served for every guest, so the number of utensils should be at least $$$24$$$: every set contains $$$4$$$ utensils and every one of the $$$3$$$ guests gets two such sets. Therefore, at least $$$14$$$ objects have been stolen. Please note that utensils of some types (for example, of types $$$2$$$ and $$$4$$$ in this example) may be not present in the set served for dishes.


Petya has an array $$$a$$$ consisting of $$$n$$$ integers. He wants to remove duplicate (equal) elements.Petya wants to leave only the rightmost entry (occurrence) for each element of the array. The relative order of the remaining unique elements should not be changed.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$) — the number of elements in Petya's array. The following line contains a sequence $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 1\,000$$$) — the Petya's array.

In the first line print integer $$$x$$$ — the number of elements which will be left in Petya's array after he removed the duplicates. In the second line print $$$x$$$ integers separated with a space — Petya's array after he removed the duplicates. For each unique element only the rightmost entry should be left.

NoteIn the first example you should remove two integers $$$1$$$, which are in the positions $$$1$$$ and $$$4$$$. Also you should remove the integer $$$5$$$, which is in the position $$$2$$$.In the second example you should remove integer $$$2$$$, which is in the position $$$1$$$, and two integers $$$4$$$, which are in the positions $$$2$$$ and $$$4$$$.In the third example you should remove four integers $$$6$$$, which are in the positions $$$1$$$, $$$2$$$, $$$3$$$ and $$$4$$$.


Little Elephant loves magic squares very much.A magic square is a 3 × 3 table, each cell contains some positive integer. At that the sums of integers in all rows, columns and diagonals of the table are equal. The figure below shows the magic square, the sum of integers in all its rows, columns and diagonals equals 15.  The Little Elephant remembered one magic square. He started writing this square on a piece of paper, but as he wrote, he forgot all three elements of the main diagonal of the magic square. Fortunately, the Little Elephant clearly remembered that all elements of the magic square did not exceed 105. Help the Little Elephant, restore the original magic square, given the Elephant's notes.

The first three lines of the input contain the Little Elephant's notes. The first line contains elements of the first row of the magic square. The second line contains the elements of the second row, the third line is for the third row. The main diagonal elements that have been forgotten by the Elephant are represented by zeroes. It is guaranteed that the notes contain exactly three zeroes and they are all located on the main diagonal. It is guaranteed that all positive numbers in the table do not exceed 105.

Print three lines, in each line print three integers — the Little Elephant's magic square. If there are multiple magic squares, you are allowed to print any of them. Note that all numbers you print must be positive and not exceed 105. It is guaranteed that there exists at least one magic square that meets the conditions.


zscoder wants to generate an input file for some programming competition problem.His input is a string consisting of n letters 'a'. He is too lazy to write a generator so he will manually generate the input in a text editor.Initially, the text editor is empty. It takes him x seconds to insert or delete a letter 'a' from the text file and y seconds to copy the contents of the entire text file, and duplicate it.zscoder wants to find the minimum amount of time needed for him to create the input file of exactly n letters 'a'. Help him to determine the amount of time needed to generate the input.

The only line contains three integers n, x and y (1 ≤ n ≤ 107, 1 ≤ x, y ≤ 109) — the number of letters 'a' in the input file and the parameters from the problem statement.

Print the only integer t — the minimum amount of time needed to generate the input file.


Igor K. always used to trust his favorite Kashpirovsky Antivirus. That is why he didn't hesitate to download the link one of his groupmates sent him via QIP Infinium. The link was said to contain "some real funny stuff about swine influenza". The antivirus had no objections and Igor K. run the flash application he had downloaded. Immediately his QIP Infinium said: "invalid login/password".Igor K. entered the ISQ from his additional account and looked at the info of his main one. His name and surname changed to "H1N1" and "Infected" correspondingly, and the "Additional Information" field contained a strange-looking binary code 80 characters in length, consisting of zeroes and ones. "I've been hacked" — thought Igor K. and run the Internet Exploiter browser to quickly type his favourite search engine's address.Soon he learned that it really was a virus that changed ISQ users' passwords. Fortunately, he soon found out that the binary code was actually the encrypted password where each group of 10 characters stood for one decimal digit. Accordingly, the original password consisted of 8 decimal digits.Help Igor K. restore his ISQ account by the encrypted password and encryption specification.

The input data contains 11 lines. The first line represents the binary code 80 characters in length. That is the code written in Igor K.'s ISQ account's info. Next 10 lines contain pairwise distinct binary codes 10 characters in length, corresponding to numbers 0, 1, ..., 9.

Print one line containing 8 characters — The password to Igor K.'s ISQ account. It is guaranteed that the solution exists.


Theatre Square in the capital city of Berland has a rectangular shape with the size n × m meters. On the occasion of the city's anniversary, a decision was taken to pave the Square with square granite flagstones. Each flagstone is of the size a × a.What is the least number of flagstones needed to pave the Square? It's allowed to cover the surface larger than the Theatre Square, but the Square has to be covered. It's not allowed to break the flagstones. The sides of flagstones should be parallel to the sides of the Square.

The input contains three positive integer numbers in the first line: n,  m and a (1 ≤  n, m, a ≤ 109).


You have two friends. You want to present each of them several positive integers. You want to present cnt1 numbers to the first friend and cnt2 numbers to the second friend. Moreover, you want all presented numbers to be distinct, that also means that no number should be presented to both friends.In addition, the first friend does not like the numbers that are divisible without remainder by prime number x. The second one does not like the numbers that are divisible without remainder by prime number y. Of course, you're not going to present your friends numbers they don't like.Your task is to find such minimum number v, that you can form presents using numbers from a set 1, 2, ..., v. Of course you may choose not to present some numbers at all.A positive integer number greater than 1 is called prime if it has no positive divisors other than 1 and itself.

The only line contains four positive integers cnt1, cnt2, x, y (1 ≤ cnt1, cnt2 < 109; cnt1 + cnt2 ≤ 109; 2 ≤ x < y ≤ 3·104) — the numbers that are described in the statement. It is guaranteed that numbers x, y are prime.

Print a single integer — the answer to the problem.

NoteIn the first sample you give the set of numbers {1, 3, 5} to the first friend and the set of numbers {2} to the second friend. Note that if you give set {1, 3, 5} to the first friend, then we cannot give any of the numbers 1, 3, 5 to the second friend. In the second sample you give the set of numbers {3} to the first friend, and the set of numbers {1, 2, 4} to the second friend. Thus, the answer to the problem is 4.


Little Petya was given this problem for homework:You are given function  (here  represents the operation of taking the remainder). His task is to count the number of integers x in range [a;b] with property f(x) = x.It is a pity that Petya forgot the order in which the remainders should be taken and wrote down only 4 numbers. Each of 24 possible orders of taking the remainder has equal probability of being chosen. For example, if Petya has numbers 1, 2, 3, 4 then he can take remainders in that order or first take remainder modulo 4, then modulo 2, 3, 1. There also are 22 other permutations of these numbers that represent orders in which remainder can be taken. In this problem 4 numbers wrote down by Petya will be pairwise distinct.Now it is impossible for Petya to complete the task given by teacher but just for fun he decided to find the number of integers  with property that probability that f(x) = x is not less than 31.4159265352718281828459045%. In other words, Petya will pick up the number x if there exist at least 7 permutations of numbers p1, p2, p3, p4, for which f(x) = x.

First line of the input will contain 6 integers, separated by spaces: p1, p2, p3, p4, a, b (1 ≤ p1, p2, p3, p4 ≤ 1000, 0 ≤ a ≤ b ≤ 31415).  It is guaranteed that numbers p1, p2, p3, p4 will be pairwise distinct.

Output the number of integers in the given range that have the given property.


Vadim loves decorating the Christmas tree, so he got a beautiful garland as a present. It consists of $$$n$$$ light bulbs in a single row. Each bulb has a number from $$$1$$$ to $$$n$$$ (in arbitrary order), such that all the numbers are distinct. While Vadim was solving problems, his home Carp removed some light bulbs from the garland. Now Vadim wants to put them back on.Vadim wants to put all bulb back on the garland. Vadim defines complexity of a garland to be the number of pairs of adjacent bulbs with numbers with different parity (remainder of the division by $$$2$$$). For example, the complexity of 1 4 2 3 5 is $$$2$$$ and the complexity of 1 3 5 7 6 4 2 is $$$1$$$.No one likes complexity, so Vadim wants to minimize the number of such pairs. Find the way to put all bulbs back on the garland, such that the complexity is as small as possible.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 100$$$) — the number of light bulbs on the garland. The second line contains $$$n$$$ integers $$$p_1,\ p_2,\ \ldots,\ p_n$$$ ($$$0 \le p_i \le n$$$) — the number on the $$$i$$$-th bulb, or $$$0$$$ if it was removed.

Output a single number — the minimum complexity of the garland.

NoteIn the first example, one should place light bulbs as 1 5 4 2 3. In that case, the complexity would be equal to 2, because only $$$(5, 4)$$$ and $$$(2, 3)$$$ are the pairs of adjacent bulbs that have different parity.In the second case, one of the correct answers is 1 7 3 5 6 4 2.


In the city of Saint Petersburg, a day lasts for $$$2^{100}$$$ minutes. From the main station of Saint Petersburg, a train departs after $$$1$$$ minute, $$$4$$$ minutes, $$$16$$$ minutes, and so on; in other words, the train departs at time $$$4^k$$$ for each integer $$$k \geq 0$$$. Team BowWow has arrived at the station at the time $$$s$$$ and it is trying to count how many trains have they missed; in other words, the number of trains that have departed strictly before time $$$s$$$. For example if $$$s = 20$$$, then they missed trains which have departed at $$$1$$$, $$$4$$$ and $$$16$$$. As you are the only one who knows the time, help them!Note that the number $$$s$$$ will be given you in a binary representation without leading zeroes.

The first line contains a single binary number $$$s$$$ ($$$0 \leq s < 2^{100}$$$) without leading zeroes.

Output a single number — the number of trains which have departed strictly before the time $$$s$$$.

NoteIn the first example $$$100000000_2 = 256_{10}$$$, missed trains have departed at $$$1$$$, $$$4$$$, $$$16$$$ and $$$64$$$.In the second example $$$101_2 = 5_{10}$$$, trains have departed at $$$1$$$ and $$$4$$$.The third example is explained in the statements.


The number "zero" is called "love" (or "l'oeuf" to be precise, literally means "egg" in French), for example when denoting the zero score in a game of tennis. Aki is fond of numbers, especially those with trailing zeros. For example, the number $$$9200$$$ has two trailing zeros. Aki thinks the more trailing zero digits a number has, the prettier it is.However, Aki believes, that the number of trailing zeros of a number is not static, but depends on the base (radix) it is represented in. Thus, he considers a few scenarios with some numbers and bases. And now, since the numbers he used become quite bizarre, he asks you to help him to calculate the beauty of these numbers.Given two integers $$$n$$$ and $$$b$$$ (in decimal notation), your task is to calculate the number of trailing zero digits in the $$$b$$$-ary (in the base/radix of $$$b$$$) representation of $$$n\,!$$$ (factorial of $$$n$$$).

The only line of the input contains two integers $$$n$$$ and $$$b$$$ ($$$1 \le n \le 10^{18}$$$, $$$2 \le b \le 10^{12}$$$).

Print an only integer — the number of trailing zero digits in the $$$b$$$-ary representation of $$$n!$$$

NoteIn the first example, $$$6!_{(10)} = 720_{(10)} = 880_{(9)}$$$.In the third and fourth example, $$$5!_{(10)} = 120_{(10)} = 1111000_{(2)}$$$.The representation of the number $$$x$$$ in the $$$b$$$-ary base is $$$d_1, d_2, \ldots, d_k$$$ if $$$x = d_1 b^{k - 1} + d_2 b^{k - 2} + \ldots + d_k b^0$$$, where $$$d_i$$$ are integers and $$$0 \le d_i \le b - 1$$$. For example, the number $$$720$$$ from the first example is represented as $$$880_{(9)}$$$ since $$$720 = 8 \cdot 9^2 + 8 \cdot 9 + 0 \cdot 1$$$.You can read more about bases here.


Vasya has n burles. One bottle of Ber-Cola costs a burles and one Bars bar costs b burles. He can buy any non-negative integer number of bottles of Ber-Cola and any non-negative integer number of Bars bars.Find out if it's possible to buy some amount of bottles of Ber-Cola and Bars bars and spend exactly n burles.In other words, you should find two non-negative integers x and y such that Vasya can buy x bottles of Ber-Cola and y Bars bars and x·a + y·b = n or tell that it's impossible.

First line contains single integer n (1 ≤ n ≤ 10 000 000) — amount of money, that Vasya has. Second line contains single integer a (1 ≤ a ≤ 10 000 000) — cost of one bottle of Ber-Cola. Third line contains single integer b (1 ≤ b ≤ 10 000 000) — cost of one Bars bar.

If Vasya can't buy Bars and Ber-Cola in such a way to spend exactly n burles print «NO» (without quotes). Otherwise in first line print «YES» (without quotes). In second line print two non-negative integers x and y — number of bottles of Ber-Cola and number of Bars bars Vasya should buy in order to spend exactly n burles, i.e. x·a + y·b = n. If there are multiple answers print any of them. Any of numbers x and y can be equal 0.

NoteIn first example Vasya can buy two bottles of Ber-Cola and one Bars bar. He will spend exactly 2·2 + 1·3 = 7 burles.In second example Vasya can spend exactly n burles multiple ways:   buy two bottles of Ber-Cola and five Bars bars;  buy four bottles of Ber-Cola and don't buy Bars bars;  don't buy Ber-Cola and buy 10 Bars bars. In third example it's impossible to but Ber-Cola and Bars bars in order to spend exactly n burles.


Pasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n. Pasha likes rectangles but hates squares, so he wonders, how many ways are there to split a stick into four parts so that it's possible to form a rectangle using these parts, but is impossible to form a square.Your task is to help Pasha and count the number of such ways. Two ways to cut the stick are considered distinct if there exists some integer x, such that the number of parts of length x in the first way differ from the number of parts of length x in the second way.

The first line of the input contains a positive integer n (1 ≤ n ≤ 2·109) — the length of Pasha's stick.

The output should contain a single integer — the number of ways to split Pasha's stick into four parts of positive integer length so that it's possible to make a rectangle by connecting the ends of these parts, but is impossible to form a square.

NoteThere is only one way to divide the stick in the first sample {1, 1, 2, 2}.Four ways to divide the stick in the second sample are {1, 1, 9, 9}, {2, 2, 8, 8}, {3, 3, 7, 7} and {4, 4, 6, 6}. Note that {5, 5, 5, 5} doesn't work.


Sarah has always been a lover of nature, and a couple of years ago she saved up enough money to travel the world and explore all the things built by nature over its lifetime on earth. During this time she visited some truly special places which were left untouched for centuries, from watching icebergs in freezing weather to scuba-diving in oceans and admiring the sea life, residing unseen. These experiences were enhanced with breathtaking views built by mountains over time and left there for visitors to see for years on end. Over time, all these expeditions took a toll on Sarah and culminated in her decision to settle down in the suburbs and live a quiet life. However, as Sarah's love for nature never faded, she started growing flowers in her garden in an attempt to stay connected with nature. At the beginning she planted only blue orchids, but over time she started using different flower types to add variety to her collection of flowers. This collection of flowers can be represented as an array of $$$N$$$ flowers and the $$$i$$$-th of them has a type associated with it, denoted as $$$A_i$$$. Each resident, passing by her collection and limited by the width of his view, can only see $$$K$$$ contiguous flowers at each moment in time. To see the whole collection, the resident will look at the first $$$K$$$ contiguous flowers $$$A_1, A_2, ..., A_K$$$, then shift his view by one flower and look at the next section of K contiguous flowers $$$A_2, A_3, ..., A_{K+1}$$$ and so on until they scan the whole collection, ending with section $$$A_{N-K+1}, ..., A_{N-1}, A_N$$$.Each resident determines the beautiness of a section of $$$K$$$ flowers as the number of distinct flower types in that section. Furthermore, the beautiness of the whole collection is calculated by summing the beautiness values of each contiguous section. Formally, beautiness $$$B_i$$$ of a section starting at the $$$i$$$-th position is calculated as $$$B_i = distinct(A_i, A_{i+1}, ..., A_{i+K-1})$$$, and beautiness of the collection $$$B$$$ is calculated as $$$B=B_1 + B_2 + ... + B_{N-K+1}$$$.In addition, as Sarah wants to keep her collection of flowers have a fresh feel, she can also pick two points $$$L$$$ and $$$R$$$, dispose flowers between those two points and plant new flowers, all of them being the same type.You will be given $$$Q$$$ queries and each of those queries will be of the following two types:   You will be given three integers $$$L, R, X$$$ describing that Sarah has planted flowers of type $$$X$$$ between positions $$$L$$$ and $$$R$$$ inclusive. Formally collection is changed such that $$$A[i]=X$$$ for all $$$i$$$ in range $$$[L.. R]$$$.  You will be given integer $$$K$$$, width of the resident's view and you have to determine the beautiness value $$$B$$$ resident has associated with the collection For each query of second type print the result – beautiness $$$B$$$ of the collection.

First line contains two integers $$$N$$$ and $$$Q \;(1 \leq N, Q \leq 10^5)\,$$$ — number of flowers and the number of queries, respectively. The second line contains $$$N$$$ integers $$$A_1, A_2, ..., A_N\;(1 \leq A_i \leq 10^9)\,$$$ — where $$$A_i$$$ represents type of the $$$i$$$-th flower. Each of the next $$$Q$$$ lines describe queries and start with integer $$$T\in\{1, 2\}$$$.    If $$$T = 1$$$, there will be three more integers in the line $$$L, R, X\;(1 \leq L, R \leq N;\; 1 \leq X \leq 10^9)\,$$$ — $$$L$$$ and $$$R$$$ describing boundaries and $$$X$$$ describing the flower type  If $$$T = 2$$$, there will be one more integer in the line $$$K\;(1 \leq K \leq N)\,$$$ — resident's width of view

For each query of the second type print the beautiness $$$B$$$ of the collection.

NoteLet's look at the example.Initially the collection is $$$[1, 2, 3, 4, 5]$$$. In the first query $$$K = 3$$$, we consider sections of three flowers with the first being $$$[1, 2, 3]$$$. Since beautiness of the section is the number of distinct flower types in that section, $$$B_1 = 3$$$. Second section is $$$[2, 3, 4]$$$ and $$$B_2 = 3$$$. Third section is $$$[3, 4, 5]$$$ and $$$B_3 = 3$$$, since the flower types are all distinct. The beautiness value resident has associated with the collection is $$$B = B_1 + B_2 + B_3 = 3 + 3 + 3 = 9$$$.After the second query, the collection becomes $$$[5, 5, 3, 4, 5]$$$. For the third query $$$K = 4$$$, so we consider sections of four flowers with the first being $$$[5, 5, 3, 4]$$$. There are three distinct flower types $$$[5, 3, 4]$$$ in this section, so $$$B_1 = 3$$$. Second section $$$[5, 3, 4, 5]$$$ also has $$$3$$$ distinct flower types, so $$$B_2 = 3$$$. The beautiness value resident has associated with the collection is $$$B = B_1 + B_2 = 3 + 3 = 6$$$After the fourth query, the collection becomes $$$[5, 5, 5, 5, 5]$$$.For the fifth query $$$K = 2$$$ and in this case all the four sections are same with each of them being $$$[5, 5]$$$. Beautiness of $$$[5, 5]$$$ is $$$1$$$ since there is only one distinct element in this section $$$[5]$$$. Beautiness of the whole collection is $$$B = B_1 + B_2 + B_3 + B_4 = 1 + 1 + 1 + 1 = 4$$$


Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."  The problem is: You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.If we sort all lucky numbers in increasing order, what's the 1-based index of n? Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.

The first and only line of input contains a lucky number n (1 ≤ n ≤ 109).

Print the index of n among all lucky numbers.


You have a fraction . You need to find the first occurrence of digit c into decimal notation of the fraction after decimal point.

The first contains three single positive integers a, b, c (1 ≤ a < b ≤ 105, 0 ≤ c ≤ 9).

Print position of the first occurrence of digit c into the fraction. Positions are numbered from 1 after decimal point. It there is no such position, print -1.

NoteThe fraction in the first example has the following decimal notation: . The first zero stands on second position.The fraction in the second example has the following decimal notation: . There is no digit 7 in decimal notation of the fraction.


Professor GukiZ makes a new robot. The robot are in the point with coordinates (x1, y1) and should go to the point (x2, y2). In a single step the robot can change any of its coordinates (maybe both of them) by one (decrease or increase). So the robot can move in one of the 8 directions. Find the minimal number of steps the robot should make to get the finish position.

The first line contains two integers x1, y1 ( - 109 ≤ x1, y1 ≤ 109) — the start position of the robot. The second line contains two integers x2, y2 ( - 109 ≤ x2, y2 ≤ 109) — the finish position of the robot.

Print the only integer d — the minimal number of steps to get the finish position.

NoteIn the first example robot should increase both of its coordinates by one four times, so it will be in position (4, 4). After that robot should simply increase its y coordinate and get the finish position.In the second example robot should simultaneously increase x coordinate and decrease y coordinate by one three times.


To quickly hire highly skilled specialists one of the new IT City companies made an unprecedented move. Every employee was granted a car, and an employee can choose one of four different car makes.The parking lot before the office consists of one line of (2n - 2) parking spaces. Unfortunately the total number of cars is greater than the parking lot capacity. Furthermore even amount of cars of each make is greater than the amount of parking spaces! That's why there are no free spaces on the parking lot ever.Looking on the straight line of cars the company CEO thought that parking lot would be more beautiful if it contained exactly n successive cars of the same make. Help the CEO determine the number of ways to fill the parking lot this way.

The only line of the input contains one integer n (3 ≤ n ≤ 30) — the amount of successive cars of the same make.

Output one integer — the number of ways to fill the parking lot by cars of four makes using the described way.

NoteLet's denote car makes in the following way: A — Aston Martin, B —   Bentley, M — Mercedes-Maybach, Z — Zaporozhets. For n = 3 there are the following appropriate ways to fill the parking lot: AAAB AAAM AAAZ ABBB AMMM AZZZ BBBA BBBM BBBZ BAAA BMMM BZZZ MMMA MMMB MMMZ MAAA MBBB MZZZ ZZZA ZZZB ZZZM ZAAA ZBBB ZMMMOriginally it was planned to grant sport cars of Ferrari, Lamborghini, Maserati and Bugatti makes but this idea was renounced because it is impossible to drive these cars having small road clearance on the worn-down roads of IT City.


The main street of Berland is a straight line with n houses built along it (n is an even number). The houses are located at both sides of the street. The houses with odd numbers are at one side of the street and are numbered from 1 to n - 1 in the order from the beginning of the street to the end (in the picture: from left to right). The houses with even numbers are at the other side of the street and are numbered from 2 to n in the order from the end of the street to its beginning (in the picture: from right to left). The corresponding houses with even and odd numbers are strictly opposite each other, that is, house 1 is opposite house n, house 3 is opposite house n - 2, house 5 is opposite house n - 4 and so on.  Vasya needs to get to house number a as quickly as possible. He starts driving from the beginning of the street and drives his car to house a. To get from the beginning of the street to houses number 1 and n, he spends exactly 1 second. He also spends exactly one second to drive the distance between two neighbouring houses. Vasya can park at any side of the road, so the distance between the beginning of the street at the houses that stand opposite one another should be considered the same.Your task is: find the minimum time Vasya needs to reach house a.

The first line of the input contains two integers, n and a (1 ≤ a ≤ n ≤ 100 000) — the number of houses on the street and the number of the house that Vasya needs to reach, correspondingly. It is guaranteed that number n is even.

Print a single integer — the minimum time Vasya needs to get from the beginning of the street to house a.

NoteIn the first sample there are only four houses on the street, two houses at each side. House 2 will be the last at Vasya's right.The second sample corresponds to picture with n = 8. House 5 is the one before last at Vasya's left.


Vadim is really keen on travelling. Recently he heard about kayaking activity near his town and became very excited about it, so he joined a party of kayakers.Now the party is ready to start its journey, but firstly they have to choose kayaks. There are 2·n people in the group (including Vadim), and they have exactly n - 1 tandem kayaks (each of which, obviously, can carry two people) and 2 single kayaks. i-th person's weight is wi, and weight is an important matter in kayaking — if the difference between the weights of two people that sit in the same tandem kayak is too large, then it can crash. And, of course, people want to distribute their seats in kayaks in order to minimize the chances that kayaks will crash.Formally, the instability of a single kayak is always 0, and the instability of a tandem kayak is the absolute difference between weights of the people that are in this kayak. Instability of the whole journey is the total instability of all kayaks.Help the party to determine minimum possible total instability!

The first line contains one number n (2 ≤ n ≤ 50). The second line contains 2·n integer numbers w1, w2, ..., w2n, where wi is weight of person i (1 ≤ wi ≤ 1000).

Print minimum possible total instability.


Vasya came up with his own weather forecasting method. He knows the information about the average air temperature for each of the last n days. Assume that the average air temperature for each day is integral.Vasya believes that if the average temperatures over the last n days form an arithmetic progression, where the first term equals to the average temperature on the first day, the second term equals to the average temperature on the second day and so on, then the average temperature of the next (n + 1)-th day will be equal to the next term of the arithmetic progression. Otherwise, according to Vasya's method, the temperature of the (n + 1)-th day will be equal to the temperature of the n-th day.Your task is to help Vasya predict the average temperature for tomorrow, i. e. for the (n + 1)-th day.

The first line contains a single integer n (2 ≤ n ≤ 100) — the number of days for which the average air temperature is known. The second line contains a sequence of integers t1, t2, ..., tn ( - 1000 ≤ ti ≤ 1000) — where ti is the average temperature in the i-th day.

Print the average air temperature in the (n + 1)-th day, which Vasya predicts according to his method. Note that the absolute value of the predicted temperature can exceed 1000.

NoteIn the first example the sequence of the average temperatures is an arithmetic progression where the first term is 10 and each following terms decreases by 5. So the predicted average temperature for the sixth day is  - 10 - 5 =  - 15.In the second example the sequence of the average temperatures is an arithmetic progression where the first term is 1 and each following terms equals to the previous one. So the predicted average temperature in the fifth day is 1.In the third example the average temperatures do not form an arithmetic progression, so the average temperature of the fourth day equals to the temperature of the third day and equals to  - 5.In the fourth example the sequence of the average temperatures is an arithmetic progression where the first term is 900 and each the following terms increase by 100. So predicted average temperature in the third day is 1000 + 100 = 1100.


At the children's festival, children were dancing in a circle. When music stopped playing, the children were still standing in a circle. Then Lena remembered, that her parents gave her a candy box with exactly $$$k$$$ candies "Wilky May". Lena is not a greedy person, so she decided to present all her candies to her friends in the circle. Lena knows, that some of her friends have a sweet tooth and others do not. Sweet tooth takes out of the box two candies, if the box has at least two candies, and otherwise takes one. The rest of Lena's friends always take exactly one candy from the box.Before starting to give candies, Lena step out of the circle, after that there were exactly $$$n$$$ people remaining there. Lena numbered her friends in a clockwise order with positive integers starting with $$$1$$$ in such a way that index $$$1$$$ was assigned to her best friend Roma.Initially, Lena gave the box to the friend with number $$$l$$$, after that each friend (starting from friend number $$$l$$$) took candies from the box and passed the box to the next friend in clockwise order. The process ended with the friend number $$$r$$$ taking the last candy (or two, who knows) and the empty box. Please note that it is possible that some of Lena's friends took candy from the box several times, that is, the box could have gone several full circles before becoming empty.Lena does not know which of her friends have a sweet tooth, but she is interested in the maximum possible number of friends that can have a sweet tooth. If the situation could not happen, and Lena have been proved wrong in her observations, please tell her about this.

The only line contains four integers $$$n$$$, $$$l$$$, $$$r$$$ and $$$k$$$ ($$$1 \le n, k \le 10^{11}$$$, $$$1 \le l, r \le n$$$) — the number of children in the circle, the number of friend, who was given a box with candies, the number of friend, who has taken last candy and the initial number of candies in the box respectively.

Print exactly one integer — the maximum possible number of sweet tooth among the friends of Lena or "-1" (quotes for clarity), if Lena is wrong.

NoteIn the first example, any two friends can be sweet tooths, this way each person will receive the box with candies twice and the last person to take sweets will be the fourth friend.In the second example, sweet tooths can be any three friends, except for the friend on the third position.In the third example, only one friend will take candy, but he can still be a sweet tooth, but just not being able to take two candies. All other friends in the circle can be sweet tooths as well, they just will not be able to take a candy even once.In the fourth example, Lena is wrong and this situation couldn't happen.


During the winter holidays, the demand for Christmas balls is exceptionally high. Since it's already 2018, the advances in alchemy allow easy and efficient ball creation by utilizing magic crystals.Grisha needs to obtain some yellow, green and blue balls. It's known that to produce a yellow ball one needs two yellow crystals, green — one yellow and one blue, and for a blue ball, three blue crystals are enough.Right now there are A yellow and B blue crystals in Grisha's disposal. Find out how many additional crystals he should acquire in order to produce the required number of balls.

The first line features two integers A and B (0 ≤ A, B ≤ 109), denoting the number of yellow and blue crystals respectively at Grisha's disposal. The next line contains three integers x, y and z (0 ≤ x, y, z ≤ 109) — the respective amounts of yellow, green and blue balls to be obtained.

Print a single integer — the minimum number of crystals that Grisha should acquire in addition.

NoteIn the first sample case, Grisha needs five yellow and four blue crystals to create two yellow balls, one green ball, and one blue ball. To do that, Grisha needs to obtain two additional crystals: one yellow and one blue.


Pak Chanek has a grid that has $$$N$$$ rows and $$$M$$$ columns. Each row is numbered from $$$1$$$ to $$$N$$$ from top to bottom. Each column is numbered from $$$1$$$ to $$$M$$$ from left to right.Each tile in the grid contains a number. The numbers are arranged as follows:   Row $$$1$$$ contains integers from $$$1$$$ to $$$M$$$ from left to right.  Row $$$2$$$ contains integers from $$$M+1$$$ to $$$2 \times M$$$ from left to right.  Row $$$3$$$ contains integers from $$$2 \times M+1$$$ to $$$3 \times M$$$ from left to right.  And so on until row $$$N$$$. A domino is defined as two different tiles in the grid that touch by their sides. A domino is said to be tight if and only if the two numbers in the domino have a difference of exactly $$$1$$$. Count the number of distinct tight dominoes in the grid.Two dominoes are said to be distinct if and only if there exists at least one tile that is in one domino, but not in the other.

The only line contains two integers $$$N$$$ and $$$M$$$ ($$$1 \leq N, M \leq 10^9$$$) — the number of rows and columns in the grid.

An integer representing the number of distinct tight dominoes in the grid.

NoteThe picture below is the grid that Pak Chanek has in the first example.  The picture below is an example of a tight domino in the grid.


Ania has a large integer $$$S$$$. Its decimal representation has length $$$n$$$ and doesn't contain any leading zeroes. Ania is allowed to change at most $$$k$$$ digits of $$$S$$$. She wants to do it in such a way that $$$S$$$ still won't contain any leading zeroes and it'll be minimal possible. What integer will Ania finish with?

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 200\,000$$$, $$$0 \leq k \leq n$$$) — the number of digits in the decimal representation of $$$S$$$ and the maximum allowed number of changed digits. The second line contains the integer $$$S$$$. It's guaranteed that $$$S$$$ has exactly $$$n$$$ digits and doesn't contain any leading zeroes.

Output the minimal possible value of $$$S$$$ which Ania can end with. Note that the resulting integer should also have $$$n$$$ digits.

NoteA number has leading zeroes if it consists of at least two digits and its first digit is $$$0$$$. For example, numbers $$$00$$$, $$$00069$$$ and $$$0101$$$ have leading zeroes, while $$$0$$$, $$$3000$$$ and $$$1010$$$ don't have leading zeroes.


Once upon a time there were several little pigs and several wolves on a two-dimensional grid of size n × m. Each cell in this grid was either empty, containing one little pig, or containing one wolf.A little pig and a wolf are adjacent if the cells that they are located at share a side. The little pigs are afraid of wolves, so there will be at most one wolf adjacent to each little pig. But each wolf may be adjacent to any number of little pigs.They have been living peacefully for several years. But today the wolves got hungry. One by one, each wolf will choose one of the little pigs adjacent to it (if any), and eats the poor little pig. This process is not repeated. That is, each wolf will get to eat at most one little pig. Once a little pig gets eaten, it disappears and cannot be eaten by any other wolf.What is the maximum number of little pigs that may be eaten by the wolves?

The first line contains integers n and m (1 ≤ n, m ≤ 10) which denotes the number of rows and columns in our two-dimensional grid, respectively. Then follow n lines containing m characters each — that is the grid description. "." means that this cell is empty. "P" means that this cell contains a little pig. "W" means that this cell contains a wolf.  It is guaranteed that there will be at most one wolf adjacent to any little pig.

Print a single number — the maximal number of little pigs that may be eaten by the wolves.

NoteIn the first example, one possible scenario in which two little pigs get eaten by the wolves is as follows.


Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Petya loves tickets very much. As we know, each ticket has a number that is a positive integer. Its length equals n (n is always even). Petya calls a ticket lucky if the ticket's number is a lucky number and the sum of digits in the first half (the sum of the first n / 2 digits) equals the sum of digits in the second half (the sum of the last n / 2 digits). Check if the given ticket is lucky.

The first line contains an even integer n (2 ≤ n ≤ 50) — the length of the ticket number that needs to be checked. The second line contains an integer whose length equals exactly n — the ticket number. The number may contain leading zeros.

On the first line print "YES" if the given ticket number is lucky. Otherwise, print "NO" (without the quotes).

NoteIn the first sample the sum of digits in the first half does not equal the sum of digits in the second half (4 ≠ 7).In the second sample the ticket number is not the lucky number.


The last stage of Football World Cup is played using the play-off system.There are n teams left in this stage, they are enumerated from 1 to n. Several rounds are held, in each round the remaining teams are sorted in the order of their ids, then the first in this order plays with the second, the third — with the fourth, the fifth — with the sixth, and so on. It is guaranteed that in each round there is even number of teams. The winner of each game advances to the next round, the loser is eliminated from the tournament, there are no draws. In the last round there is the only game with two remaining teams: the round is called the Final, the winner is called the champion, and the tournament is over.Arkady wants his two favorite teams to play in the Final. Unfortunately, the team ids are already determined, and it may happen that it is impossible for teams to meet in the Final, because they are to meet in some earlier stage, if they are strong enough. Determine, in which round the teams with ids a and b can meet.

The only line contains three integers n, a and b (2 ≤ n ≤ 256, 1 ≤ a, b ≤ n) — the total number of teams, and the ids of the teams that Arkady is interested in.  It is guaranteed that n is such that in each round an even number of team advance, and that a and b are not equal.

In the only line print "Final!" (without quotes), if teams a and b can meet in the Final. Otherwise, print a single integer — the number of the round in which teams a and b can meet. The round are enumerated from 1.

NoteIn the first example teams 1 and 2 meet in the first round.In the second example teams 2 and 6 can only meet in the third round, which is the Final, if they win all their opponents in earlier rounds.In the third example the teams with ids 7 and 5 can meet in the second round, if they win their opponents in the first round.


Monocarp is playing a video game. In the game, he controls a spaceship and has to destroy an enemy spaceship.Monocarp has two lasers installed on his spaceship. Both lasers $$$1$$$ and $$$2$$$ have two values:   $$$p_i$$$ — the power of the laser;  $$$t_i$$$ — the reload time of the laser. When a laser is fully charged, Monocarp can either shoot it or wait for the other laser to charge and shoot both of them at the same time.An enemy spaceship has $$$h$$$ durability and $$$s$$$ shield capacity. When Monocarp shoots an enemy spaceship, it receives $$$(P - s)$$$ damage (i. e. $$$(P - s)$$$ gets subtracted from its durability), where $$$P$$$ is the total power of the lasers that Monocarp shoots (i. e. $$$p_i$$$ if he only shoots laser $$$i$$$ and $$$p_1 + p_2$$$ if he shoots both lasers at the same time). An enemy spaceship is considered destroyed when its durability becomes $$$0$$$ or lower.Initially, both lasers are zero charged.What's the lowest amount of time it can take Monocarp to destroy an enemy spaceship?

The first line contains two integers $$$p_1$$$ and $$$t_1$$$ ($$$2 \le p_1 \le 5000$$$; $$$1 \le t_1 \le 10^{12}$$$) — the power and the reload time of the first laser. The second line contains two integers $$$p_2$$$ and $$$t_2$$$ ($$$2 \le p_2 \le 5000$$$; $$$1 \le t_2 \le 10^{12}$$$) — the power and the reload time of the second laser. The third line contains two integers $$$h$$$ and $$$s$$$ ($$$1 \le h \le 5000$$$; $$$1 \le s < \min(p_1, p_2)$$$) — the durability and the shield capacity of an enemy spaceship. Note that the last constraint implies that Monocarp will always be able to destroy an enemy spaceship.

Print a single integer — the lowest amount of time it can take Monocarp to destroy an enemy spaceship.

NoteIn the first example, Monocarp waits for both lasers to charge, then shoots both lasers at $$$10$$$, they deal $$$(5 + 4 - 1) = 8$$$ damage. Then he waits again and shoots lasers at $$$20$$$, dealing $$$8$$$ more damage.In the second example, Monocarp doesn't wait for the second laser to charge. He just shoots the first laser $$$25$$$ times, dealing $$$(10 - 9) = 1$$$ damage each time.


Your task is the exact same as for the easy version. But this time, the marmots subtract the village's population P from their random number before responding to Heidi's request.Also, there are now villages with as few as a single inhabitant, meaning that .Can you help Heidi find out whether a village follows a Poisson or a uniform distribution?

Same as for the easy and medium versions. But remember that now 1 ≤ P ≤ 1000 and that the marmots may provide positive as well as negative integers.

Output one line per village, in the same order as provided in the input. The village's line shall state poisson if the village's distribution is of the Poisson type, and uniform if the answers came from a uniform distribution.


Vasilisa the Wise from the Kingdom of Far Far Away got a magic box with a secret as a present from her friend Hellawisa the Wise from the Kingdom of A Little Closer. However, Vasilisa the Wise does not know what the box's secret is, since she cannot open it again. She hopes that you will help her one more time with that.The box's lock looks as follows: it contains 4 identical deepenings for gems as a 2 × 2 square, and some integer numbers are written at the lock's edge near the deepenings. The example of a lock is given on the picture below.  The box is accompanied with 9 gems. Their shapes match the deepenings' shapes and each gem contains one number from 1 to 9 (each number is written on exactly one gem). The box will only open after it is decorated with gems correctly: that is, each deepening in the lock should be filled with exactly one gem. Also, the sums of numbers in the square's rows, columns and two diagonals of the square should match the numbers written at the lock's edge. For example, the above lock will open if we fill the deepenings with gems with numbers as is shown on the picture below.  Now Vasilisa the Wise wants to define, given the numbers on the box's lock, which gems she should put in the deepenings to open the box. Help Vasilisa to solve this challenging task.

The input contains numbers written on the edges of the lock of the box. The first line contains space-separated integers r1 and r2 that define the required sums of numbers in the rows of the square. The second line contains space-separated integers c1 and c2 that define the required sums of numbers in the columns of the square. The third line contains space-separated integers d1 and d2 that define the required sums of numbers on the main and on the side diagonals of the square (1 ≤ r1, r2, c1, c2, d1, d2 ≤ 20). Correspondence between the above 6 variables and places where they are written is shown on the picture below. For more clarifications please look at the second sample test that demonstrates the example given in the problem statement.

Print the scheme of decorating the box with stones: two lines containing two space-separated integers from 1 to 9. The numbers should be pairwise different. If there is no solution for the given lock, then print the single number "-1" (without the quotes). If there are several solutions, output any.

NotePay attention to the last test from the statement: it is impossible to open the box because for that Vasilisa the Wise would need 4 identical gems containing number "5". However, Vasilisa only has one gem with each number from 1 to 9.


wHAT DO WE NEED cAPS LOCK FOR?Caps lock is a computer keyboard key. Pressing it sets an input mode in which typed letters are capital by default. If it is pressed by accident, it leads to accidents like the one we had in the first passage. Let's consider that a word has been typed with the Caps lock key accidentally switched on, if:   either it only contains uppercase letters;  or all letters except for the first one are uppercase. In this case we should automatically change the case of all letters. For example, the case of the letters that form words "hELLO", "HTTP", "z" should be changed.Write a program that applies the rule mentioned above. If the rule cannot be applied, the program should leave the word unchanged.

The first line of the input data contains a word consisting of uppercase and lowercase Latin letters. The word's length is from 1 to 100 characters, inclusive.

Print the result of the given word's processing.


There are n walruses sitting in a circle. All of them are numbered in the clockwise order: the walrus number 2 sits to the left of the walrus number 1, the walrus number 3 sits to the left of the walrus number 2, ..., the walrus number 1 sits to the left of the walrus number n.The presenter has m chips. The presenter stands in the middle of the circle and starts giving the chips to the walruses starting from walrus number 1 and moving clockwise. The walrus number i gets i chips. If the presenter can't give the current walrus the required number of chips, then the presenter takes the remaining chips and the process ends. Determine by the given n and m how many chips the presenter will get in the end.

The first line contains two integers n and m (1 ≤ n ≤ 50, 1 ≤ m ≤ 104) — the number of walruses and the number of chips correspondingly.

Print the number of chips the presenter ended up with.

NoteIn the first sample the presenter gives one chip to the walrus number 1, two chips to the walrus number 2, three chips to the walrus number 3, four chips to the walrus number 4, then again one chip to the walrus number 1. After that the presenter runs out of chips. He can't give anything to the walrus number 2 and the process finishes.In the third sample the presenter gives one chip to the walrus number 1, two chips to the walrus number 2, three chips to the walrus number 3, then again one chip to the walrus number 1. The presenter has one chip left and he can't give two chips to the walrus number 2, that's why the presenter takes the last chip.


The only difference between this problem and D2 is that you don't have to provide the way to construct the answer in this problem, but you have to do it in D2.There's a table of $$$n \times m$$$ cells ($$$n$$$ rows and $$$m$$$ columns). The value of $$$n \cdot m$$$ is even.A domino is a figure that consists of two cells having a common side. It may be horizontal (one of the cells is to the right of the other) or vertical (one of the cells is above the other).You need to find out whether it is possible to place $$$\frac{nm}{2}$$$ dominoes on the table so that exactly $$$k$$$ of them are horizontal and all the other dominoes are vertical. The dominoes cannot overlap and must fill the whole table.

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10$$$) — the number of test cases. Then $$$t$$$ test cases follow. Each test case consists of a single line. The line contains three integers $$$n$$$, $$$m$$$, $$$k$$$ ($$$1 \le n,m \le 100$$$, $$$0 \le k \le \frac{nm}{2}$$$, $$$n \cdot m$$$ is even) — the number of rows, columns and horizontal dominoes, respectively.

For each test case output "YES", if it is possible to place dominoes in the desired way, or "NO" otherwise. You may print each letter in any case (YES, yes, Yes will all be recognized as positive answer, NO, no and nO will all be recognized as negative answer).


There are two sisters Alice and Betty. You have $$$n$$$ candies. You want to distribute these $$$n$$$ candies between two sisters in such a way that:  Alice will get $$$a$$$ ($$$a > 0$$$) candies;  Betty will get $$$b$$$ ($$$b > 0$$$) candies;  each sister will get some integer number of candies;  Alice will get a greater amount of candies than Betty (i.e. $$$a > b$$$);  all the candies will be given to one of two sisters (i.e. $$$a+b=n$$$). Your task is to calculate the number of ways to distribute exactly $$$n$$$ candies between sisters in a way described above. Candies are indistinguishable.Formally, find the number of ways to represent $$$n$$$ as the sum of $$$n=a+b$$$, where $$$a$$$ and $$$b$$$ are positive integers and $$$a>b$$$.You have to answer $$$t$$$ independent test cases.

The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Then $$$t$$$ test cases follow. The only line of a test case contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^9$$$) — the number of candies you have.

For each test case, print the answer — the number of ways to distribute exactly $$$n$$$ candies between two sisters in a way described in the problem statement. If there is no way to satisfy all the conditions, print $$$0$$$.

NoteFor the test case of the example, the $$$3$$$ possible ways to distribute candies are:  $$$a=6$$$, $$$b=1$$$;  $$$a=5$$$, $$$b=2$$$;  $$$a=4$$$, $$$b=3$$$.


Alice and Bob have decided to play the game "Rock, Paper, Scissors". The game consists of several rounds, each round is independent of each other. In each round, both players show one of the following things at the same time: rock, paper or scissors. If both players showed the same things then the round outcome is a draw. Otherwise, the following rules applied:  if one player showed rock and the other one showed scissors, then the player who showed rock is considered the winner and the other one is considered the loser;  if one player showed scissors and the other one showed paper, then the player who showed scissors is considered the winner and the other one is considered the loser;  if one player showed paper and the other one showed rock, then the player who showed paper is considered the winner and the other one is considered the loser. Alice and Bob decided to play exactly $$$n$$$ rounds of the game described above. Alice decided to show rock $$$a_1$$$ times, show scissors $$$a_2$$$ times and show paper $$$a_3$$$ times. Bob decided to show rock $$$b_1$$$ times, show scissors $$$b_2$$$ times and show paper $$$b_3$$$ times. Though, both Alice and Bob did not choose the sequence in which they show things. It is guaranteed that $$$a_1 + a_2 + a_3 = n$$$ and $$$b_1 + b_2 + b_3 = n$$$.Your task is to find two numbers:  the minimum number of round Alice can win;  the maximum number of rounds Alice can win.

The first line of the input contains one integer $$$n$$$ ($$$1 \le n \le 10^{9}$$$) — the number of rounds. The second line of the input contains three integers $$$a_1, a_2, a_3$$$ ($$$0 \le a_i \le n$$$) — the number of times Alice will show rock, scissors and paper, respectively. It is guaranteed that $$$a_1 + a_2 + a_3 = n$$$. The third line of the input contains three integers $$$b_1, b_2, b_3$$$ ($$$0 \le b_j \le n$$$) — the number of times Bob will show rock, scissors and paper, respectively. It is guaranteed that $$$b_1 + b_2 + b_3 = n$$$.

Print two integers: the minimum and the maximum number of rounds Alice can win.

NoteIn the first example, Alice will not win any rounds if she shows scissors and then paper and Bob shows rock and then scissors. In the best outcome, Alice will win one round if she shows paper and then scissors, and Bob shows rock and then scissors.In the second example, Alice will not win any rounds if Bob shows the same things as Alice each round.In the third example, Alice always shows paper and Bob always shows rock so Alice will win all three rounds anyway.


Student Andrey has been skipping physical education lessons for the whole term, and now he must somehow get a passing grade on this subject. Obviously, it is impossible to do this by legal means, but Andrey doesn't give up. Having obtained an empty certificate from a local hospital, he is going to use his knowledge of local doctor's handwriting to make a counterfeit certificate of illness. However, after writing most of the certificate, Andrey suddenly discovered that doctor's signature is impossible to forge. Or is it?For simplicity, the signature is represented as an $$$n\times m$$$ grid, where every cell is either filled with ink or empty. Andrey's pen can fill a $$$3\times3$$$ square without its central cell if it is completely contained inside the grid, as shown below. xxxx.xxxx Determine whether is it possible to forge the signature on an empty $$$n\times m$$$ grid.

The first line of input contains two integers $$$n$$$ and $$$m$$$ ($$$3 \le n, m \le 1000$$$). Then $$$n$$$ lines follow, each contains $$$m$$$ characters. Each of the characters is either '.', representing an empty cell, or '#', representing an ink filled cell.

If Andrey can forge the signature, output "YES". Otherwise output "NO". You can print each letter in any case (upper or lower).

NoteIn the first sample Andrey can paint the border of the square with the center in $$$(2, 2)$$$.In the second sample the signature is impossible to forge.In the third sample Andrey can paint the borders of the squares with the centers in $$$(2, 2)$$$ and $$$(3, 2)$$$:   we have a clear paper: ............  use the pen with center at $$$(2, 2)$$$. ####.####...  use the pen with center at $$$(3, 2)$$$. ############ In the fourth sample Andrey can paint the borders of the squares with the centers in $$$(3, 3)$$$ and $$$(3, 5)$$$.


A little girl loves problems on bitwise operations very much. Here's one of them.You are given two integers l and r. Let's consider the values of  for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.Expression  means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".

The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018). Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

In a single line print a single integer — the maximum value of  for all pairs of integers a, b (l ≤ a ≤ b ≤ r).


Eighth-grader Vova is on duty today in the class. After classes, he went into the office to wash the board, and found on it the number n. He asked what is this number and the teacher of mathematics Inna Petrovna answered Vova that n is the answer to the arithmetic task for first-graders. In the textbook, a certain positive integer x was given. The task was to add x to the sum of the digits of the number x written in decimal numeral system.Since the number n on the board was small, Vova quickly guessed which x could be in the textbook. Now he wants to get a program which will search for arbitrary values of the number n for all suitable values of x or determine that such x does not exist. Write such a program for Vova.

The first line contains integer n (1 ≤ n ≤ 109).

In the first line print one integer k — number of different values of x satisfying the condition.  In next k lines print these values in ascending order.

NoteIn the first test case x = 15 there is only one variant: 15 + 1 + 5 = 21.In the second test case there are no such x.


Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:  start the race from some point of a field,  go around the flag,  close cycle returning back to the starting point. Polycarp knows the coordinates of the starting point (x1, y1) and the coordinates of the point where the flag is situated (x2, y2). Polycarp’s quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x, y) to any of four points: (x - 1, y), (x + 1, y), (x, y - 1) or (x, y + 1).Thus the quadcopter path is a closed cycle starting and finishing in (x1, y1) and containing the point (x2, y2) strictly inside.    The picture corresponds to the first example: the starting (and finishing) point is in (1, 5) and the flag is in (5, 2). What is the minimal length of the quadcopter path?

The first line contains two integer numbers x1 and y1 ( - 100 ≤ x1, y1 ≤ 100) — coordinates of the quadcopter starting (and finishing) point. The second line contains two integer numbers x2 and y2 ( - 100 ≤ x2, y2 ≤ 100) — coordinates of the flag. It is guaranteed that the quadcopter starting point and the flag do not coincide.

Print the length of minimal path of the quadcopter to surround the flag and return back.


Petya and Vasya decided to play a game. They have n cards (n is an even number). A single integer is written on each card.Before the game Petya will choose an integer and after that Vasya will choose another integer (different from the number that Petya chose). During the game each player takes all the cards with number he chose. For example, if Petya chose number 5 before the game he will take all cards on which 5 is written and if Vasya chose number 10 before the game he will take all cards on which 10 is written.The game is considered fair if Petya and Vasya can take all n cards, and the number of cards each player gets is the same.Determine whether Petya and Vasya can choose integer numbers before the game so that the game is fair.

The first line contains a single integer n (2 ≤ n ≤ 100) — number of cards. It is guaranteed that n is an even number. The following n lines contain a sequence of integers a1, a2, ..., an (one integer per line, 1 ≤ ai ≤ 100) — numbers written on the n cards.

If it is impossible for Petya and Vasya to choose numbers in such a way that the game will be fair, print "NO" (without quotes) in the first line. In this case you should not print anything more. In the other case print "YES" (without quotes) in the first line. In the second line print two distinct integers — number that Petya should choose and the number that Vasya should choose to make the game fair. If there are several solutions, print any of them.

NoteIn the first example the game will be fair if, for example, Petya chooses number 11, and Vasya chooses number 27. Then the will take all cards — Petya will take cards 1 and 4, and Vasya will take cards 2 and 3. Thus, each of them will take exactly two cards.In the second example fair game is impossible because the numbers written on the cards are equal, but the numbers that Petya and Vasya should choose should be distinct.In the third example it is impossible to take all cards. Petya and Vasya can take at most five cards — for example, Petya can choose number 10 and Vasya can choose number 20. But for the game to be fair it is necessary to take 6 cards.


Galois is one of the strongest chess players of Byteforces. He has even invented a new variant of chess, which he named «PawnChess».This new game is played on a board consisting of 8 rows and 8 columns. At the beginning of every game some black and white pawns are placed on the board. The number of black pawns placed is not necessarily equal to the number of white pawns placed.   Lets enumerate rows and columns with integers from 1 to 8. Rows are numbered from top to bottom, while columns are numbered from left to right. Now we denote as (r, c) the cell located at the row r and at the column c.There are always two players A and B playing the game. Player A plays with white pawns, while player B plays with black ones. The goal of player A is to put any of his pawns to the row 1, while player B tries to put any of his pawns to the row 8. As soon as any of the players completes his goal the game finishes immediately and the succeeded player is declared a winner.Player A moves first and then they alternate turns. On his move player A must choose exactly one white pawn and move it one step upward and player B (at his turn) must choose exactly one black pawn and move it one step down. Any move is possible only if the targeted cell is empty. It's guaranteed that for any scenario of the game there will always be at least one move available for any of the players.Moving upward means that the pawn located in (r, c) will go to the cell (r - 1, c), while moving down means the pawn located in (r, c) will go to the cell (r + 1, c). Again, the corresponding cell must be empty, i.e. not occupied by any other pawn of any color.Given the initial disposition of the board, determine who wins the game if both players play optimally. Note that there will always be a winner due to the restriction that for any game scenario both players will have some moves available.

The input consists of the board description given in eight lines, each line contains eight characters. Character 'B' is used to denote a black pawn, and character 'W' represents a white pawn. Empty cell is marked with '.'.  It's guaranteed that there will not be white pawns on the first row neither black pawns on the last row.

Print 'A' if player A wins the game on the given board, and 'B' if player B will claim the victory. Again, it's guaranteed that there will always be a winner on the given board.

NoteIn the first sample player A is able to complete his goal in 3 steps by always moving a pawn initially located at (4, 5). Player B needs at least 5 steps for any of his pawns to reach the row 8. Hence, player A will be the winner.


There are r red and g green blocks for construction of the red-green tower. Red-green tower can be built following next rules:  Red-green tower is consisting of some number of levels;  Let the red-green tower consist of n levels, then the first level of this tower should consist of n blocks, second level — of n - 1 blocks, the third one — of n - 2 blocks, and so on — the last level of such tower should consist of the one block. In other words, each successive level should contain one block less than the previous one;  Each level of the red-green tower should contain blocks of the same color.  Let h be the maximum possible number of levels of red-green tower, that can be built out of r red and g green blocks meeting the rules above. The task is to determine how many different red-green towers having h levels can be built out of the available blocks.Two red-green towers are considered different if there exists some level, that consists of red blocks in the one tower and consists of green blocks in the other tower.You are to write a program that will find the number of different red-green towers of height h modulo 109 + 7.

The only line of input contains two integers r and g, separated by a single space — the number of available red and green blocks respectively (0 ≤ r, g ≤ 2·105, r + g ≥ 1).

Output the only integer — the number of different possible red-green towers of height h modulo 109 + 7.

NoteThe image in the problem statement shows all possible red-green towers for the first sample.


Recently, Berland faces federalization requests more and more often. The proponents propose to divide the country into separate states. Moreover, they demand that there is a state which includes exactly k towns.Currently, Berland has n towns, some pairs of them are connected by bilateral roads. Berland has only n - 1 roads. You can reach any city from the capital, that is, the road network forms a tree.The Ministry of Roads fears that after the reform those roads that will connect the towns of different states will bring a lot of trouble.Your task is to come up with a plan to divide the country into states such that:  each state is connected, i.e. for each state it is possible to get from any town to any other using its roads (that is, the roads that connect the state towns),  there is a state that consisted of exactly k cities,  the number of roads that connect different states is minimum.

The first line contains integers n, k (1 ≤ k ≤ n ≤ 400). Then follow n - 1 lines, each of them describes a road in Berland. The roads are given as pairs of integers xi, yi (1 ≤ xi, yi ≤ n; xi ≠ yi) — the numbers of towns connected by the road. Assume that the towns are numbered from 1 to n.

The the first line print the required minimum number of "problem" roads t. Then print a sequence of t integers — their indices in the found division. The roads are numbered starting from 1 in the order they follow in the input. If there are multiple possible solutions, print any of them. If the solution shows that there are no "problem" roads at all, print a single integer 0 and either leave the second line empty or do not print it at all.


Polycarpus has got n candies and m friends (n ≥ m). He wants to make a New Year present with candies to each friend. Polycarpus is planning to present all candies and he wants to do this in the fairest (that is, most equal) manner. He wants to choose such ai, where ai is the number of candies in the i-th friend's present, that the maximum ai differs from the least ai as little as possible.For example, if n is divisible by m, then he is going to present the same number of candies to all his friends, that is, the maximum ai won't differ from the minimum one.

The single line of the input contains a pair of space-separated positive integers n, m (1 ≤ n, m ≤ 100;n ≥ m) — the number of candies and the number of Polycarpus's friends.

Print the required sequence a1, a2, ..., am, where ai is the number of candies in the i-th friend's present. All numbers ai must be positive integers, total up to n, the maximum one should differ from the minimum one by the smallest possible value.

NotePrint ai in any order, separate the numbers by spaces.


For an array of integers $$$a$$$, let's define $$$|a|$$$ as the number of elements in it.Let's denote two functions: $$$F(a, k)$$$ is a function that takes an array of integers $$$a$$$ and a positive integer $$$k$$$. The result of this function is the array containing $$$|a|$$$ first elements of the array that you get by replacing each element of $$$a$$$ with exactly $$$k$$$ copies of that element.For example, $$$F([2, 2, 1, 3, 5, 6, 8], 2)$$$ is calculated as follows: first, you replace each element of the array with $$$2$$$ copies of it, so you obtain $$$[2, 2, 2, 2, 1, 1, 3, 3, 5, 5, 6, 6, 8, 8]$$$. Then, you take the first $$$7$$$ elements of the array you obtained, so the result of the function is $$$[2, 2, 2, 2, 1, 1, 3]$$$. $$$G(a, x, y)$$$ is a function that takes an array of integers $$$a$$$ and two different integers $$$x$$$ and $$$y$$$. The result of this function is the array $$$a$$$ with every element equal to $$$x$$$ replaced by $$$y$$$, and every element equal to $$$y$$$ replaced by $$$x$$$.For example, $$$G([1, 1, 2, 3, 5], 3, 1) = [3, 3, 2, 1, 5]$$$.An array $$$a$$$ is a parent of the array $$$b$$$ if:  either there exists a positive integer $$$k$$$ such that $$$F(a, k) = b$$$;  or there exist two different integers $$$x$$$ and $$$y$$$ such that $$$G(a, x, y) = b$$$. An array $$$a$$$ is an ancestor of the array $$$b$$$ if there exists a finite sequence of arrays $$$c_0, c_1, \dots, c_m$$$ ($$$m \ge 0$$$) such that $$$c_0$$$ is $$$a$$$, $$$c_m$$$ is $$$b$$$, and for every $$$i \in [1, m]$$$, $$$c_{i-1}$$$ is a parent of $$$c_i$$$.And now, the problem itself.You are given two integers $$$n$$$ and $$$k$$$. Your goal is to construct a sequence of arrays $$$s_1, s_2, \dots, s_m$$$ in such a way that:  every array $$$s_i$$$ contains exactly $$$n$$$ elements, and all elements are integers from $$$1$$$ to $$$k$$$;  for every array $$$a$$$ consisting of exactly $$$n$$$ integers from $$$1$$$ to $$$k$$$, the sequence contains at least one array $$$s_i$$$ such that $$$s_i$$$ is an ancestor of $$$a$$$. Print the minimum number of arrays in such sequence.

The only line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n, k \le 2 \cdot 10^5$$$).

Print one integer — the minimum number of elements in a sequence of arrays meeting the constraints. Since the answer can be large, output it modulo $$$998244353$$$.


Your security guard friend recently got a new job at a new security company. The company requires him to patrol an area of the city encompassing exactly N city blocks, but they let him choose which blocks. That is, your friend must walk the perimeter of a region whose area is exactly N blocks. Your friend is quite lazy and would like your help to find the shortest possible route that meets the requirements. The city is laid out in a square grid pattern, and is large enough that for the sake of the problem it can be considered infinite.

Input will consist of a single integer N (1 ≤ N ≤ 106), the number of city blocks that must be enclosed by the route.

Print the minimum perimeter that can be achieved.

NoteHere are some possible shapes for the examples:


Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.

The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).

If it's impossible to find the representation of n as a product of k numbers, print -1. Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.


A and B are preparing themselves for programming contests.An important part of preparing for a competition is sharing programming knowledge from the experienced members to those who are just beginning to deal with the contests. Therefore, during the next team training A decided to make teams so that newbies are solving problems together with experienced participants.A believes that the optimal team of three people should consist of one experienced participant and two newbies. Thus, each experienced participant can share the experience with a large number of people.However, B believes that the optimal team should have two experienced members plus one newbie. Thus, each newbie can gain more knowledge and experience.As a result, A and B have decided that all the teams during the training session should belong to one of the two types described above. Furthermore, they agree that the total number of teams should be as much as possible.There are n experienced members and m newbies on the training session. Can you calculate what maximum number of teams can be formed?

The first line contains two integers n and m (0 ≤ n, m ≤ 5·105) — the number of experienced participants and newbies that are present at the training session.

Print the maximum number of teams that can be formed.

NoteLet's represent the experienced players as XP and newbies as NB.In the first test the teams look as follows: (XP, NB, NB), (XP, NB, NB).In the second test sample the teams look as follows: (XP, NB, NB), (XP, NB, NB), (XP, XP, NB).


Not so long ago the Codecraft-17 contest was held on Codeforces. The top 25 participants, and additionally random 25 participants out of those who got into top 500, will receive a Codeforces T-shirt.Unfortunately, you didn't manage to get into top 25, but you got into top 500, taking place p.Now the elimination round of 8VC Venture Cup 2017 is being held. It has been announced that the Codecraft-17 T-shirt winners will be chosen as follows. Let s be the number of points of the winner of the elimination round of 8VC Venture Cup 2017. Then the following pseudocode will be executed: i := (s div 50) mod 475repeat 25 times:    i := (i * 96 + 42) mod 475    print (26 + i)Here "div" is the integer division operator, "mod" is the modulo (the remainder of division) operator.As the result of pseudocode execution, 25 integers between 26 and 500, inclusive, will be printed. These will be the numbers of places of the participants who get the Codecraft-17 T-shirts. It is guaranteed that the 25 printed integers will be pairwise distinct for any value of s.You're in the lead of the elimination round of 8VC Venture Cup 2017, having x points. You believe that having at least y points in the current round will be enough for victory.To change your final score, you can make any number of successful and unsuccessful hacks. A successful hack brings you 100 points, an unsuccessful one takes 50 points from you. It's difficult to do successful hacks, though.You want to win the current round and, at the same time, ensure getting a Codecraft-17 T-shirt. What is the smallest number of successful hacks you have to do to achieve that?

The only line contains three integers p, x and y (26 ≤ p ≤ 500; 1 ≤ y ≤ x ≤ 20000) — your place in Codecraft-17, your current score in the elimination round of 8VC Venture Cup 2017, and the smallest number of points you consider sufficient for winning the current round.

Output a single integer — the smallest number of successful hacks you have to do in order to both win the elimination round of 8VC Venture Cup 2017 and ensure getting a Codecraft-17 T-shirt. It's guaranteed that your goal is achievable for any valid input data.

NoteIn the first example, there is no need to do any hacks since 10880 points already bring the T-shirt to the 239-th place of Codecraft-17 (that is, you). In this case, according to the pseudocode, the T-shirts will be given to the participants at the following places: 475 422 84 411 453 210 157 294 146 188 420 367 29 356 398 155 102 239 91 133 365 312 449 301 343In the second example, you have to do two successful and one unsuccessful hack to make your score equal to 7408.In the third example, you need to do as many as 24 successful hacks to make your score equal to 10400.In the fourth example, it's sufficient to do 6 unsuccessful hacks (and no successful ones) to make your score equal to 6500, which is just enough for winning the current round and also getting the T-shirt.


You may have heard of the pie rule before. It states that if two people wish to fairly share a slice of pie, one person should cut the slice in half, and the other person should choose who gets which slice. Alice and Bob have many slices of pie, and rather than cutting the slices in half, each individual slice will be eaten by just one person.The way Alice and Bob decide who eats each slice is as follows. First, the order in which the pies are to be handed out is decided. There is a special token called the "decider" token, initially held by Bob. Until all the pie is handed out, whoever has the decider token will give the next slice of pie to one of the participants, and the decider token to the other participant. They continue until no slices of pie are left.All of the slices are of excellent quality, so each participant obviously wants to maximize the total amount of pie they get to eat. Assuming both players make their decisions optimally, how much pie will each participant receive?

Input will begin with an integer N (1 ≤ N ≤ 50), the number of slices of pie.  Following this is a line with N integers indicating the sizes of the slices (each between 1 and 100000, inclusive), in the order in which they must be handed out.

Print two integers. First, the sum of the sizes of slices eaten by Alice, then the sum of the sizes of the slices eaten by Bob, assuming both players make their decisions optimally.

NoteIn the first example, Bob takes the size 141 slice for himself and gives the decider token to Alice. Then Alice gives the size 592 slice to Bob and keeps the decider token for herself, so that she can then give the size 653 slice to herself.


Shapur was an extremely gifted student. He was great at everything including Combinatorics, Algebra, Number Theory, Geometry, Calculus, etc. He was not only smart but extraordinarily fast! He could manage to sum 1018 numbers in a single second.One day in 230 AD Shapur was trying to find out if any one can possibly do calculations faster than him. As a result he made a very great contest and asked every one to come and take part.In his contest he gave the contestants many different pairs of numbers. Each number is made from digits 0 or 1. The contestants should write a new number corresponding to the given pair of numbers. The rule is simple: The i-th digit of the answer is 1 if and only if the i-th digit of the two given numbers differ. In the other case the i-th digit of the answer is 0.Shapur made many numbers and first tried his own speed. He saw that he can perform these operations on numbers of length ∞ (length of a number is number of digits in it) in a glance! He always gives correct answers so he expects the contestants to give correct answers, too. He is a good fellow so he won't give anyone very big numbers and he always gives one person numbers of same length.Now you are going to take part in Shapur's contest. See if you are faster and more accurate.

There are two lines in each input. Each of them contains a single number. It is guaranteed that the numbers are made from 0 and 1 only and that their length is same. The numbers may start with 0. The length of each number doesn't exceed 100.

Write one line — the corresponding answer. Do not omit the leading 0s.


Several months later Alex finally got his brother Bob's creation by post. And now, in his turn, Alex wants to boast about something to his brother. He thought for a while, and came to the conclusion that he has no ready creations, and decided to write a program for rectangles detection. According to his plan, the program detects if the four given segments form a rectangle of a positive area and with sides parallel to coordinate axes. As Alex does badly at school and can't write this program by himself, he asks you to help him.

The input data contain four lines. Each of these lines contains four integers x1, y1, x2, y2 ( - 109 ≤ x1, y1, x2, y2 ≤ 109) — coordinates of segment's beginning and end positions. The given segments can degenerate into points.

Output the word «YES», if the given four segments form the required rectangle, otherwise output «NO».


This is the easy version of the problem. The only difference is that in this version $$$q=1$$$. You can make hacks only if all versions of the problem are solved.Zookeeper has been teaching his $$$q$$$ sheep how to write and how to add. The $$$i$$$-th sheep has to write exactly $$$k$$$ non-negative integers with the sum $$$n_i$$$.Strangely, sheep have superstitions about digits and believe that the digits $$$3$$$, $$$6$$$, and $$$9$$$ are lucky. To them, the fortune of a number depends on the decimal representation of the number; the fortune of a number is equal to the sum of fortunes of its digits, and the fortune of a digit depends on its value and position and can be described by the following table. For example, the number $$$319$$$ has fortune $$$F_{2} + 3F_{0}$$$.   Each sheep wants to maximize the sum of fortune among all its $$$k$$$ written integers. Can you help them?

The first line contains a single integer $$$k$$$ ($$$1 \leq k \leq 999999$$$): the number of numbers each sheep has to write.   The next line contains six integers $$$F_0$$$, $$$F_1$$$, $$$F_2$$$, $$$F_3$$$, $$$F_4$$$, $$$F_5$$$ ($$$1 \leq F_i \leq 10^9$$$): the fortune assigned to each digit.   The next line contains a single integer $$$q$$$ ($$$q = 1$$$): the number of sheep. Each of the next $$$q$$$ lines contains a single integer $$$n_i$$$ ($$$1 \leq n_i \leq 999999$$$): the sum of numbers that $$$i$$$-th sheep has to write. In this version, there is only one line.

Print $$$q$$$ lines, where the $$$i$$$-th line contains the maximum sum of fortune of all numbers of the $$$i$$$-th sheep. In this version, you should print only one line.

NoteIn the first test case, $$$57 = 9 + 9 + 39$$$. The three $$$9$$$'s contribute $$$1 \cdot 3$$$ and $$$3$$$ at the tens position contributes $$$2 \cdot 1$$$. Hence the sum of fortune is $$$11$$$.In the second test case, $$$63 = 35 + 19 + 9$$$. The sum of fortune is $$$8$$$.


You are given an array of $$$n$$$ integers: $$$a_1, a_2, \ldots, a_n$$$. Your task is to find some non-zero integer $$$d$$$ ($$$-10^3 \leq d \leq 10^3$$$) such that, after each number in the array is divided by $$$d$$$, the number of positive numbers that are presented in the array is greater than or equal to half of the array size (i.e., at least $$$\lceil\frac{n}{2}\rceil$$$). Note that those positive numbers do not need to be an integer (e.g., a $$$2.5$$$ counts as a positive number). If there are multiple values of $$$d$$$ that satisfy the condition, you may print any of them. In case that there is no such $$$d$$$, print a single integer $$$0$$$.Recall that $$$\lceil x \rceil$$$ represents the smallest integer that is not less than $$$x$$$ and that zero ($$$0$$$) is neither positive nor negative.

The first line contains one integer $$$n$$$ ($$$1 \le n \le 100$$$) — the number of elements in the array. The second line contains $$$n$$$ space-separated integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^3 \le a_i \le 10^3$$$).

Print one integer $$$d$$$ ($$$-10^3 \leq d \leq 10^3$$$ and $$$d \neq 0$$$) that satisfies the given condition. If there are multiple values of $$$d$$$ that satisfy the condition, you may print any of them. In case that there is no such $$$d$$$, print a single integer $$$0$$$.

NoteIn the first sample, $$$n = 5$$$, so we need at least $$$\lceil\frac{5}{2}\rceil = 3$$$ positive numbers after division. If $$$d = 4$$$, the array after division is $$$[2.5, 0, -1.75, 0.5, 1.5]$$$, in which there are $$$3$$$ positive numbers (namely: $$$2.5$$$, $$$0.5$$$, and $$$1.5$$$).In the second sample, there is no valid $$$d$$$, so $$$0$$$ should be printed.


You are given a positive integer $$$n$$$.Let $$$S(x)$$$ be sum of digits in base 10 representation of $$$x$$$, for example, $$$S(123) = 1 + 2 + 3 = 6$$$, $$$S(0) = 0$$$.Your task is to find two integers $$$a, b$$$, such that $$$0 \leq a, b \leq n$$$, $$$a + b = n$$$ and $$$S(a) + S(b)$$$ is the largest possible among all such pairs.

The only line of input contains an integer $$$n$$$ $$$(1 \leq n \leq 10^{12})$$$.

Print largest $$$S(a) + S(b)$$$ among all pairs of integers $$$a, b$$$, such that $$$0 \leq a, b \leq n$$$ and $$$a + b = n$$$.

NoteIn the first example, you can choose, for example, $$$a = 17$$$ and $$$b = 18$$$, so that $$$S(17) + S(18) = 1 + 7 + 1 + 8 = 17$$$. It can be shown that it is impossible to get a larger answer.In the second test example, you can choose, for example, $$$a = 5000000001$$$ and $$$b = 4999999999$$$, with $$$S(5000000001) + S(4999999999) = 91$$$. It can be shown that it is impossible to get a larger answer.


There are three doors in front of you, numbered from $$$1$$$ to $$$3$$$ from left to right. Each door has a lock on it, which can only be opened with a key with the same number on it as the number on the door.There are three keys — one for each door. Two of them are hidden behind the doors, so that there is no more than one key behind each door. So two doors have one key behind them, one door doesn't have a key behind it. To obtain a key hidden behind a door, you should first unlock that door. The remaining key is in your hands.Can you open all the doors?

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 18$$$) — the number of testcases. The first line of each testcase contains a single integer $$$x$$$ ($$$1 \le x \le 3$$$) — the number on the key in your hands. The second line contains three integers $$$a, b$$$ and $$$c$$$ ($$$0 \le a, b, c \le 3$$$) — the number on the key behind each of the doors. If there is no key behind the door, the number is equal to $$$0$$$. Values $$$1, 2$$$ and $$$3$$$ appear exactly once among $$$x, a, b$$$ and $$$c$$$.

For each testcase, print "YES" if you can open all the doors. Otherwise, print "NO".


Consider the following equation:  where sign [a] represents the integer part of number a.Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.

The first line contains a single integer n (1 ≤ n ≤ 40).

Print a single integer — the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.


Kyoya Ootori is selling photobooks of the Ouran High School Host Club. He has 26 photos, labeled "a" to "z", and he has compiled them into a photo booklet with some photos in some order (possibly with some photos being duplicated). A photo booklet can be described as a string of lowercase letters, consisting of the photos in the booklet in order. He now wants to sell some "special edition" photobooks, each with one extra photo inserted anywhere in the book. He wants to make as many distinct photobooks as possible, so he can make more money. He asks Haruhi, how many distinct photobooks can he make by inserting one extra photo into the photobook he already has?Please help Haruhi solve this problem.

The first line of input will be a single string s (1 ≤ |s| ≤ 20). String s consists only of lowercase English letters.

Output a single integer equal to the number of distinct photobooks Kyoya Ootori can make.

NoteIn the first case, we can make 'ab','ac',...,'az','ba','ca',...,'za', and 'aa', producing a total of 51 distinct photo booklets.


A string a of length m is called antipalindromic iff m is even, and for each i (1 ≤ i ≤ m) ai ≠ am - i + 1.Ivan has a string s consisting of n lowercase Latin letters; n is even. He wants to form some string t that will be an antipalindromic permutation of s. Also Ivan has denoted the beauty of index i as bi, and the beauty of t as the sum of bi among all indices i such that si = ti.Help Ivan to determine maximum possible beauty of t he can get.

The first line contains one integer n (2 ≤ n ≤ 100, n is even) — the number of characters in s. The second line contains the string s itself. It consists of only lowercase Latin letters, and it is guaranteed that its letters can be reordered to form an antipalindromic string. The third line contains n integer numbers b1, b2, ..., bn (1 ≤ bi ≤ 100), where bi is the beauty of index i.

Print one number — the maximum possible beauty of t.


This is the easy version of the problem. The difference between the versions is in the constraints on the array elements. You can make hacks only if all versions of the problem are solved.You are given an array $$$[a_1, a_2, \dots, a_n]$$$. Your goal is to find the length of the longest subarray of this array such that the most frequent value in it is not unique. In other words, you are looking for a subarray such that if the most frequent value occurs $$$f$$$ times in this subarray, then at least $$$2$$$ different values should occur exactly $$$f$$$ times.An array $$$c$$$ is a subarray of an array $$$d$$$ if $$$c$$$ can be obtained from $$$d$$$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 200\,000$$$) — the length of the array. The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le min(n, 100)$$$) — elements of the array.

You should output exactly one integer  — the length of the longest subarray of the array whose most frequent value is not unique. If there is no such subarray, output $$$0$$$.

NoteIn the first sample, the subarray $$$[1, 1, 2, 2, 3, 3]$$$ is good, but $$$[1, 1, 2, 2, 3, 3, 3]$$$ isn't: in the latter there are $$$3$$$ occurrences of number $$$3$$$, and no other element appears $$$3$$$ times.


Two players are playing a game. First each of them writes an integer from 1 to 6, and then a dice is thrown. The player whose written number got closer to the number on the dice wins. If both payers have the same difference, it's a draw.The first player wrote number a, the second player wrote number b. How many ways to throw a dice are there, at which the first player wins, or there is a draw, or the second player wins?

The single line contains two integers a and b (1 ≤ a, b ≤ 6) — the numbers written on the paper by the first and second player, correspondingly.

Print three integers: the number of ways to throw the dice at which the first player wins, the game ends with a draw or the second player wins, correspondingly.

NoteThe dice is a standard cube-shaped six-sided object with each side containing a number from 1 to 6, and where all numbers on all sides are distinct.You can assume that number a is closer to number x than number b, if |a - x| < |b - x|.


Cucumber boy is fan of Kyubeat, a famous music game.Kyubeat has 16 panels for playing arranged in 4 × 4 table. When a panel lights up, he has to press that panel.Each panel has a timing to press (the preffered time when a player should press it), and Cucumber boy is able to press at most k panels in a time with his one hand. Cucumber boy is trying to press all panels in perfect timing, that is he wants to press each panel exactly in its preffered time. If he cannot press the panels with his two hands in perfect timing, his challenge to press all the panels in perfect timing will fail.You are given one scene of Kyubeat's panel from the music Cucumber boy is trying. Tell him is he able to press all the panels in perfect timing.

The first line contains a single integer k (1 ≤ k ≤ 5) — the number of panels Cucumber boy can press with his one hand. Next 4 lines contain 4 characters each (digits from 1 to 9, or period) — table of panels. If a digit i was written on the panel, it means the boy has to press that panel in time i. If period was written on the panel, he doesn't have to press that panel.

Output "YES" (without quotes), if he is able to press all the panels in perfect timing. If not, output "NO" (without quotes).

NoteIn the third sample boy cannot press all panels in perfect timing. He can press all the panels in timing in time 1, but he cannot press the panels in time 2 in timing with his two hands.


Note that the memory limit in this problem is lower than in others.You have a vertical strip with $$$n$$$ cells, numbered consecutively from $$$1$$$ to $$$n$$$ from top to bottom.You also have a token that is initially placed in cell $$$n$$$. You will move the token up until it arrives at cell $$$1$$$.Let the token be in cell $$$x > 1$$$ at some moment. One shift of the token can have either of the following kinds:   Subtraction: you choose an integer $$$y$$$ between $$$1$$$ and $$$x-1$$$, inclusive, and move the token from cell $$$x$$$ to cell $$$x - y$$$.  Floored division: you choose an integer $$$z$$$ between $$$2$$$ and $$$x$$$, inclusive, and move the token from cell $$$x$$$ to cell $$$\lfloor \frac{x}{z} \rfloor$$$ ($$$x$$$ divided by $$$z$$$ rounded down). Find the number of ways to move the token from cell $$$n$$$ to cell $$$1$$$ using one or more shifts, and print it modulo $$$m$$$. Note that if there are several ways to move the token from one cell to another in one shift, all these ways are considered distinct (check example explanation for a better understanding).

The only line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 4 \cdot 10^6$$$; $$$10^8 < m < 10^9$$$; $$$m$$$ is a prime number) — the length of the strip and the modulo.

Print the number of ways to move the token from cell $$$n$$$ to cell $$$1$$$, modulo $$$m$$$.

NoteIn the first test, there are three ways to move the token from cell $$$3$$$ to cell $$$1$$$ in one shift: using subtraction of $$$y = 2$$$, or using division by $$$z = 2$$$ or $$$z = 3$$$.There are also two ways to move the token from cell $$$3$$$ to cell $$$1$$$ via cell $$$2$$$: first subtract $$$y = 1$$$, and then either subtract $$$y = 1$$$ again or divide by $$$z = 2$$$.Therefore, there are five ways in total.