meetforever/GRPO_CL huggingface dataset:
user: You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle). 

Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.


-----Input-----

The first line contains a single integer n (1 ≤ n ≤ 5). Next n lines contain four integers each, describing a single rectangle: x_1, y_1, x_2, y_2 (0 ≤ x_1 < x_2 ≤ 31400, 0 ≤ y_1 < y_2 ≤ 31400) — x_1 and x_2 are x-coordinates of the left and right edges of the rectangle, and y_1 and y_2 are y-coordinates of the bottom and top edges of the rectangle. 

No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).


-----Output-----

In a single line print "YES", if the given rectangles form a square, or "NO" otherwise.


-----Examples-----
Input
5
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5
2 2 3 3

Output
YES

Input
4
0 0 2 3
0 3 3 5
2 0 5 2
3 2 5 5

Output
NO
user: Ivan likes to learn different things about numbers, but he is especially interested in really big numbers. Ivan thinks that a positive integer number x is really big if the difference between x and the sum of its digits (in decimal representation) is not less than s. To prove that these numbers may have different special properties, he wants to know how rare (or not rare) they are — in fact, he needs to calculate the quantity of really big numbers that are not greater than n.

Ivan tried to do the calculations himself, but soon realized that it's too difficult for him. So he asked you to help him in calculations.


-----Input-----

The first (and the only) line contains two integers n and s (1 ≤ n, s ≤ 10^18).


-----Output-----

Print one integer — the quantity of really big numbers that are not greater than n.


-----Examples-----
Input
12 1

Output
3

Input
25 20

Output
0

Input
10 9

Output
1



-----Note-----

In the first example numbers 10, 11 and 12 are really big.

In the second example there are no really big numbers that are not greater than 25 (in fact, the first really big number is 30: 30 - 3 ≥ 20).

In the third example 10 is the only really big number (10 - 1 ≥ 9).
user: You are given n points on Cartesian plane. Every point is a lattice point (i. e. both of its coordinates are integers), and all points are distinct.

You may draw two straight lines (not necessarily distinct). Is it possible to do this in such a way that every point lies on at least one of these lines?


-----Input-----

The first line contains one integer n (1 ≤ n ≤ 10^5) — the number of points you are given.

Then n lines follow, each line containing two integers x_{i} and y_{i} (|x_{i}|, |y_{i}| ≤ 10^9)— coordinates of i-th point. All n points are distinct.


-----Output-----

If it is possible to draw two straight lines in such a way that each of given points belongs to at least one of these lines, print YES. Otherwise, print NO.


-----Examples-----
Input
5
0 0
0 1
1 1
1 -1
2 2

Output
YES

Input
5
0 0
1 0
2 1
1 1
2 3

Output
NO



-----Note-----

In the first example it is possible to draw two lines, the one containing the points 1, 3 and 5, and another one containing two remaining points. [Image]
user: Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.

Memory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)^2t games in total. Since the answer can be very large, you should print it modulo 10^9 + 7. Please solve this problem for Memory.


-----Input-----

The first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.


-----Output-----

Print the number of possible games satisfying the conditions modulo 1 000 000 007 (10^9 + 7) in one line.


-----Examples-----
Input
1 2 2 1

Output
6

Input
1 1 1 2

Output
31

Input
2 12 3 1

Output
0



-----Note-----

In the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.
user: Valery is a PE teacher at a school in Berland. Soon the students are going to take a test in long jumps, and Valery has lost his favorite ruler! 

However, there is no reason for disappointment, as Valery has found another ruler, its length is l centimeters. The ruler already has n marks, with which he can make measurements. We assume that the marks are numbered from 1 to n in the order they appear from the beginning of the ruler to its end. The first point coincides with the beginning of the ruler and represents the origin. The last mark coincides with the end of the ruler, at distance l from the origin. This ruler can be repesented by an increasing sequence a_1, a_2, ..., a_{n}, where a_{i} denotes the distance of the i-th mark from the origin (a_1 = 0, a_{n} = l).

Valery believes that with a ruler he can measure the distance of d centimeters, if there is a pair of integers i and j (1 ≤ i ≤ j ≤ n), such that the distance between the i-th and the j-th mark is exactly equal to d (in other words, a_{j} - a_{i} = d). 

Under the rules, the girls should be able to jump at least x centimeters, and the boys should be able to jump at least y (x < y) centimeters. To test the children's abilities, Valery needs a ruler to measure each of the distances x and y. 

Your task is to determine what is the minimum number of additional marks you need to add on the ruler so that they can be used to measure the distances x and y. Valery can add the marks at any integer non-negative distance from the origin not exceeding the length of the ruler.


-----Input-----

The first line contains four positive space-separated integers n, l, x, y (2 ≤ n ≤ 10^5, 2 ≤ l ≤ 10^9, 1 ≤ x < y ≤ l) — the number of marks, the length of the ruler and the jump norms for girls and boys, correspondingly.

The second line contains a sequence of n integers a_1, a_2, ..., a_{n} (0 = a_1 < a_2 < ... < a_{n} = l), where a_{i} shows the distance from the i-th mark to the origin.


-----Output-----

In the first line print a single non-negative integer v — the minimum number of marks that you need to add on the ruler.

In the second line print v space-separated integers p_1, p_2, ..., p_{v} (0 ≤ p_{i} ≤ l). Number p_{i} means that the i-th mark should be at the distance of p_{i} centimeters from the origin. Print the marks in any order. If there are multiple solutions, print any of them.


-----Examples-----
Input
3 250 185 230
0 185 250

Output
1
230

Input
4 250 185 230
0 20 185 250

Output
0

Input
2 300 185 230
0 300

Output
2
185 230



-----Note-----

In the first sample it is impossible to initially measure the distance of 230 centimeters. For that it is enough to add a 20 centimeter mark or a 230 centimeter mark.

In the second sample you already can use the ruler to measure the distances of 185 and 230 centimeters, so you don't have to add new marks.

In the third sample the ruler only contains the initial and the final marks. We will need to add two marks to be able to test the children's skills.
user: As you know, every birthday party has a cake! This time, Babaei is going to prepare the very special birthday party's cake.

Simple cake is a cylinder of some radius and height. The volume of the simple cake is equal to the volume of corresponding cylinder. Babaei has n simple cakes and he is going to make a special cake placing some cylinders on each other.

However, there are some additional culinary restrictions. The cakes are numbered in such a way that the cake number i can be placed only on the table or on some cake number j where j < i. Moreover, in order to impress friends Babaei will put the cake i on top of the cake j only if the volume of the cake i is strictly greater than the volume of the cake j.

Babaei wants to prepare a birthday cake that has a maximum possible total volume. Help him find this value.


-----Input-----

The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of simple cakes Babaei has.

Each of the following n lines contains two integers r_{i} and h_{i} (1 ≤ r_{i}, h_{i} ≤ 10 000), giving the radius and height of the i-th cake.


-----Output-----

Print the maximum volume of the cake that Babaei can make. Your answer will be considered correct if its absolute or relative error does not exceed 10^{ - 6}.

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if $\frac{|a - b|}{\operatorname{max}(1, b)} \leq 10^{-6}$.


-----Examples-----
Input
2
100 30
40 10

Output
942477.796077000

Input
4
1 1
9 7
1 4
10 7

Output
3983.539484752



-----Note-----

In first sample, the optimal way is to choose the cake number 1.

In second sample, the way to get the maximum volume is to use cakes with indices 1, 2 and 4.
user: There is a toy building consisting of $n$ towers. Each tower consists of several cubes standing on each other. The $i$-th tower consists of $h_i$ cubes, so it has height $h_i$.

Let's define operation slice on some height $H$ as following: for each tower $i$, if its height is greater than $H$, then remove some top cubes to make tower's height equal to $H$. Cost of one "slice" equals to the total number of removed cubes from all towers.

Let's name slice as good one if its cost is lower or equal to $k$ ($k \ge n$).

 [Image] 

Calculate the minimum number of good slices you have to do to make all towers have the same height. Of course, it is always possible to make it so.


-----Input-----

The first line contains two integers $n$ and $k$ ($1 \le n \le 2 \cdot 10^5$, $n \le k \le 10^9$) — the number of towers and the restriction on slices, respectively.

The second line contains $n$ space separated integers $h_1, h_2, \dots, h_n$ ($1 \le h_i \le 2 \cdot 10^5$) — the initial heights of towers.


-----Output-----

Print one integer — the minimum number of good slices you have to do to make all towers have the same heigth.


-----Examples-----
Input
5 5
3 1 2 2 4

Output
2

Input
4 5
2 3 4 5

Output
2



-----Note-----

In the first example it's optimal to make $2$ slices. The first slice is on height $2$ (its cost is $3$), and the second one is on height $1$ (its cost is $4$).
user: Alice and Bob are playing yet another card game. This time the rules are the following. There are $n$ cards lying in a row in front of them. The $i$-th card has value $a_i$. 

First, Alice chooses a non-empty consecutive segment of cards $[l; r]$ ($l \le r$). After that Bob removes a single card $j$ from that segment $(l \le j \le r)$. The score of the game is the total value of the remaining cards on the segment $(a_l + a_{l + 1} + \dots + a_{j - 1} + a_{j + 1} + \dots + a_{r - 1} + a_r)$. In particular, if Alice chooses a segment with just one element, then the score after Bob removes the only card is $0$.

Alice wants to make the score as big as possible. Bob takes such a card that the score is as small as possible.

What segment should Alice choose so that the score is maximum possible? Output the maximum score.


-----Input-----

The first line contains a single integer $n$ ($1 \le n \le 10^5$) — the number of cards.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($-30 \le a_i \le 30$) — the values on the cards.


-----Output-----

Print a single integer — the final score of the game.


-----Examples-----
Input
5
5 -2 10 -1 4

Output
6

Input
8
5 2 5 3 -30 -30 6 9

Output
10

Input
3
-10 6 -15

Output
0



-----Note-----

In the first example Alice chooses a segment $[1;5]$ — the entire row of cards. Bob removes card $3$ with the value $10$ from the segment. Thus, the final score is $5 + (-2) + (-1) + 4 = 6$.

In the second example Alice chooses a segment $[1;4]$, so that Bob removes either card $1$ or $3$ with the value $5$, making the answer $5 + 2 + 3 = 10$.

In the third example Alice can choose any of the segments of length $1$: $[1;1]$, $[2;2]$ or $[3;3]$. Bob removes the only card, so the score is $0$. If Alice chooses some other segment then the answer will be less than $0$.
user: Mishka is decorating the Christmas tree. He has got three garlands, and all of them will be put on the tree. After that Mishka will switch these garlands on.

When a garland is switched on, it periodically changes its state — sometimes it is lit, sometimes not. Formally, if i-th garland is switched on during x-th second, then it is lit only during seconds x, x + k_{i}, x + 2k_{i}, x + 3k_{i} and so on.

Mishka wants to switch on the garlands in such a way that during each second after switching the garlands on there would be at least one lit garland. Formally, Mishka wants to choose three integers x_1, x_2 and x_3 (not necessarily distinct) so that he will switch on the first garland during x_1-th second, the second one — during x_2-th second, and the third one — during x_3-th second, respectively, and during each second starting from max(x_1, x_2, x_3) at least one garland will be lit.

Help Mishka by telling him if it is possible to do this!


-----Input-----

The first line contains three integers k_1, k_2 and k_3 (1 ≤ k_{i} ≤ 1500) — time intervals of the garlands.


-----Output-----

If Mishka can choose moments of time to switch on the garlands in such a way that each second after switching the garlands on at least one garland will be lit, print YES.

Otherwise, print NO.


-----Examples-----
Input
2 2 3

Output
YES

Input
4 2 3

Output
NO



-----Note-----

In the first example Mishka can choose x_1 = 1, x_2 = 2, x_3 = 1. The first garland will be lit during seconds 1, 3, 5, 7, ..., the second — 2, 4, 6, 8, ..., which already cover all the seconds after the 2-nd one. It doesn't even matter what x_3 is chosen. Our choice will lead third to be lit during seconds 1, 4, 7, 10, ..., though.

In the second example there is no way to choose such moments of time, there always be some seconds when no garland is lit.
user: You are given a string $s$ of length $n$ consisting of lowercase Latin letters. You may apply some operations to this string: in one operation you can delete some contiguous substring of this string, if all letters in the substring you delete are equal. For example, after deleting substring bbbb from string abbbbaccdd we get the string aaccdd.

Calculate the minimum number of operations to delete the whole string $s$.


-----Input-----

The first line contains one integer $n$ ($1 \le n \le 500$) — the length of string $s$.

The second line contains the string $s$ ($|s| = n$) consisting of lowercase Latin letters.


-----Output-----

Output a single integer — the minimal number of operation to delete string $s$.


-----Examples-----
Input
5
abaca

Output
3
Input
8
abcddcba

Output
4
user: The Berland State University is hosting a ballroom dance in celebration of its 100500-th anniversary! n boys and m girls are already busy rehearsing waltz, minuet, polonaise and quadrille moves.

We know that several boy&girl pairs are going to be invited to the ball. However, the partners' dancing skill in each pair must differ by at most one.

For each boy, we know his dancing skills. Similarly, for each girl we know her dancing skills. Write a code that can determine the largest possible number of pairs that can be formed from n boys and m girls.


-----Input-----

The first line contains an integer n (1 ≤ n ≤ 100) — the number of boys. The second line contains sequence a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 100), where a_{i} is the i-th boy's dancing skill.

Similarly, the third line contains an integer m (1 ≤ m ≤ 100) — the number of girls. The fourth line contains sequence b_1, b_2, ..., b_{m} (1 ≤ b_{j} ≤ 100), where b_{j} is the j-th girl's dancing skill.


-----Output-----

Print a single number — the required maximum possible number of pairs.


-----Examples-----
Input
4
1 4 6 2
5
5 1 5 7 9

Output
3

Input
4
1 2 3 4
4
10 11 12 13

Output
0

Input
5
1 1 1 1 1
3
1 2 3

Output
2
user: Kicker (table football) is a board game based on football, in which players control the footballers' figures mounted on rods by using bars to get the ball into the opponent's goal. When playing two on two, one player of each team controls the goalkeeper and the full-backs (plays defence), the other player controls the half-backs and forwards (plays attack).

Two teams of company Q decided to battle each other. Let's enumerate players from both teams by integers from 1 to 4. The first and second player play in the first team, the third and the fourth one play in the second team. For each of the four players we know their game skills in defence and attack. The defence skill of the i-th player is a_{i}, the attack skill is b_{i}.

Before the game, the teams determine how they will play. First the players of the first team decide who will play in the attack, and who will play in the defence. Then the second team players do the same, based on the choice of their opponents.

We will define a team's defence as the defence skill of player of the team who plays defence. Similarly, a team's attack is the attack skill of the player of the team who plays attack. We assume that one team is guaranteed to beat the other one, if its defence is strictly greater than the opponent's attack and its attack is strictly greater than the opponent's defence.

The teams of company Q know each other's strengths and therefore arrange their teams optimally. Identify the team that is guaranteed to win (if both teams act optimally) or tell that there is no such team.


-----Input-----

The input contain the players' description in four lines. The i-th line contains two space-separated integers a_{i} and b_{i} (1 ≤ a_{i}, b_{i} ≤ 100) — the defence and the attack skill of the i-th player, correspondingly.


-----Output-----

If the first team can win, print phrase "Team 1" (without the quotes), if the second team can win, print phrase "Team 2" (without the quotes). If no of the teams can definitely win, print "Draw" (without the quotes).


-----Examples-----
Input
1 100
100 1
99 99
99 99

Output
Team 1

Input
1 1
2 2
3 3
2 2

Output
Team 2

Input
3 3
2 2
1 1
2 2

Output
Draw



-----Note-----

Let consider the first test sample. The first team can definitely win if it will choose the following arrangement: the first player plays attack, the second player plays defence.

Consider the second sample. The order of the choosing roles for players makes sense in this sample. As the members of the first team choose first, the members of the second team can beat them (because they know the exact defence value and attack value of the first team).
user: Takahashi wants to grill N pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the i-th piece of meat are \left(x_i, y_i\right), and its hardness is c_i.
Takahashi can use one heat source to grill the meat. If he puts the heat source at coordinates \left(X, Y\right), where X and Y are real numbers, the i-th piece of meat will be ready to eat in c_i \times \sqrt{\left(X - x_i\right)^2 + \left(Y-y_i\right)^2} seconds.
Takahashi wants to eat K pieces of meat. Find the time required to have K or more pieces of meat ready if he put the heat source to minimize this time.

-----Constraints-----
 - All values in input are integers.
 - 1 \leq N \leq 60
 - 1 \leq K \leq N
 - -1000 \leq x_i , y_i \leq 1000
 - \left(x_i, y_i\right) \neq \left(x_j, y_j\right) \left(i \neq j \right)
 - 1 \leq c_i \leq 100

-----Input-----
Input is given from Standard Input in the following format:
N K
x_1 y_1 c_1
\vdots
x_N y_N c_N

-----Output-----
Print the answer.
It will be considered correct if its absolute or relative error from our answer is at most 10^{-6}.

-----Sample Input-----
4 3
-1 0 3
0 0 3
1 0 2
1 1 40

-----Sample Output-----
2.4

If we put the heat source at \left(-0.2, 0\right), the 1-st, 2-nd, and 3-rd pieces of meat will be ready to eat within 2.4 seconds. This is the optimal place to put the heat source.
user: Monocarp and Bicarp live in Berland, where every bus ticket consists of $n$ digits ($n$ is an even number). During the evening walk Monocarp and Bicarp found a ticket where some of the digits have been erased. The number of digits that have been erased is even.

Monocarp and Bicarp have decided to play a game with this ticket. Monocarp hates happy tickets, while Bicarp collects them. A ticket is considered happy if the sum of the first $\frac{n}{2}$ digits of this ticket is equal to the sum of the last $\frac{n}{2}$ digits.

Monocarp and Bicarp take turns (and Monocarp performs the first of them). During each turn, the current player must replace any erased digit with any digit from $0$ to $9$. The game ends when there are no erased digits in the ticket.

If the ticket is happy after all erased digits are replaced with decimal digits, then Bicarp wins. Otherwise, Monocarp wins. You have to determine who will win if both players play optimally.


-----Input-----

The first line contains one even integer $n$ $(2 \le n \le 2 \cdot 10^{5})$ — the number of digits in the ticket.

The second line contains a string of $n$ digits and "?" characters — the ticket which Monocarp and Bicarp have found. If the $i$-th character is "?", then the $i$-th digit is erased. Note that there may be leading zeroes. The number of "?" characters is even.


-----Output-----

If Monocarp wins, print "Monocarp" (without quotes). Otherwise print "Bicarp" (without quotes).


-----Examples-----
Input
4
0523

Output
Bicarp

Input
2
??

Output
Bicarp

Input
8
?054??0?

Output
Bicarp

Input
6
???00?

Output
Monocarp



-----Note-----

Since there is no question mark in the ticket in the first example, the winner is determined before the game even starts, and it is Bicarp.

In the second example, Bicarp also wins. After Monocarp chooses an erased digit and replaces it with a new one, Bicap can choose another position with an erased digit and replace it with the same digit, so the ticket is happy.