vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
In this challenge, the task is to debug the existing code to successfully execute all provided test files.

There are $n$ boxes in front of you. For each $\boldsymbol{i}$, box $\boldsymbol{i}$ contains $r[i]$ red balls, $g[i]$ green balls, and $b[i]$ blue balls. 

You want to separate the balls by their color. In each operation, you can pick a single ball from some box and put it into another box. The balls are separated if no box contains balls of more than one color.

Debug the given function min_operations and compute the minimal number of operations required to separate the balls.

Note: In this problem you can modify at most six lines of code and you cannot add any new lines.

To restore the original code, click on the icon to the right of the language selector.

Input Format

The first line contains a single integer $n$.
The next $n$ lines $\boldsymbol{i}$ contain three space-separated integers, $r[i]$, $g[i]$, and $b[i]$, respectively.

Constraints

$1\leq n\leq100$ 

$0\leq r[i],\ g[i],\ b[i]\leq105$ 

Output Format

Print the minimal number of operations required to separate the balls. If this is impossible, return $-1$.

Sample Input
3
1 1 1
1 1 1
1 1 1

Sample Output
6

Explanation

Each box contains 1 ball of each color.  In this explanation, the goal will be to let the first box contain only red balls, the second box only blue balls, and the third box only green balls.   

Move 1 blue ball and 1 green ball from the first box to the second and third boxes.   
Move 1 red ball and 1 green ball from the second box to the first and third boxes.   
Move 1 red ball and 1 blue ball from the third box to the first and second boxes.   

The number of operations is 6.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Gleb And Pizza

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Gleb ordered pizza home. When the courier delivered the pizza, he was very upset, because several pieces of sausage lay on the crust, and he does not really like the crust.

The pizza is a circle of radius *r* and center at the origin. Pizza consists of the main part — circle of radius *r*<=-<=*d* with center at the origin, and crust around the main part of the width *d*. Pieces of sausage are also circles. The radius of the *i* -th piece of the sausage is *r**i*, and the center is given as a pair (*x**i*, *y**i*).

Gleb asks you to help determine the number of pieces of sausage caught on the crust. A piece of sausage got on the crust, if it completely lies on the crust.

Input Specification:
First string contains two integer numbers *r* and *d* (0<=≤<=*d*<=&lt;<=*r*<=≤<=500) — the radius of pizza and the width of crust.

Next line contains one integer number *n* — the number of pieces of sausage (1<=≤<=*n*<=≤<=105).

Each of next *n* lines contains three integer numbers *x**i*, *y**i* and *r**i* (<=-<=500<=≤<=*x**i*,<=*y**i*<=≤<=500, 0<=≤<=*r**i*<=≤<=500), where *x**i* and *y**i* are coordinates of the center of *i*-th peace of sausage, *r**i* — radius of *i*-th peace of sausage.

Output Specification:
Output the number of pieces of sausage that lay on the crust.

Demo Input:
['8 4\n7\n7 8 1\n-7 3 2\n0 2 1\n0 -2 2\n-3 -3 1\n0 6 2\n5 3 1\n', '10 8\n4\n0 0 9\n0 0 10\n1 0 1\n1 0 2\n']

Demo Output:
['2\n', '0\n']

Note:
Below is a picture explaining the first example. Circles of green color denote pieces of sausage lying on the crust.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
This problem is same as the next one, but has smaller constraints.

It was a Sunday morning when the three friends Selena, Shiro and Katie decided to have a trip to the nearby power station (do not try this at home). After arriving at the power station, the cats got impressed with a large power transmission system consisting of many chimneys, electric poles, and wires. Since they are cats, they found those things gigantic.

At the entrance of the station, there is a map describing the complicated wiring system. Selena is the best at math among three friends. He decided to draw the map on the Cartesian plane. Each pole is now a point at some coordinates $(x_i, y_i)$. Since every pole is different, all of the points representing these poles are distinct. Also, every two poles are connected with each other by wires. A wire is a straight line on the plane infinite in both directions. If there are more than two poles lying on the same line, they are connected by a single common wire.

Selena thinks, that whenever two different electric wires intersect, they may interfere with each other and cause damage. So he wonders, how many pairs are intersecting? Could you help him with this problem?


-----Input-----

The first line contains a single integer $n$ ($2 \le n \le 50$) — the number of electric poles.

Each of the following $n$ lines contains two integers $x_i$, $y_i$ ($-10^4 \le x_i, y_i \le 10^4$) — the coordinates of the poles.

It is guaranteed that all of these $n$ points are distinct.


-----Output-----

Print a single integer — the number of pairs of wires that are intersecting.


-----Examples-----
Input
4
0 0
1 1
0 3
1 2

Output
14

Input
4
0 0
0 2
0 4
2 0

Output
6

Input
3
-1 -1
1 0
3 1

Output
0



-----Note-----

In the first example: [Image] 

In the second example: [Image] 

Note that the three poles $(0, 0)$, $(0, 2)$ and $(0, 4)$ are connected by a single wire.

In the third example: [Image]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The campus is abuzz with synapse fever and the synapse committee is planning a new game this year.The rules are simple enough and you have to outsmart other players to win it.
You will be given a string containing only digits between 1 and 9(both inclusive).
You can divide the string in segments such that for every segment formed,the sum of digits in that segment should be less than or equal to the sum of digits in the segment to the right of it.
You may not divide the string and thus keep only one segment.There is no constraint on the number of divisions.
Your task is to give the total number of  possibilities of such divisions or segments from the given string.

Input

First line will contain single integer 1 ≤ n ≤ 70 denoting number of test cases.
For every test case a single string of length 1 ≤ l ≤ 50.

Output

For every test case output single integer denoting total number of  possibilities of divisions or segments from the given string.

Sample:

Input

1

9876

Output

2

Explanation:
There are only two possible outcomes
(i)No division so the segment is 9876
(ii)One division after 9,so segments are 9 and 876,where (9) ≤ (8+7+6).
Thus ans is 2.

SAMPLE INPUT
1
9876

SAMPLE OUTPUT
2

Explanation

There are only two possible outcomes
(i)No division so the segment is 9876
(ii)One division after 9,so segments are 9 and 876,where (9) ≤ (8+7+6).
Thus ans is 2.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an array arr of size N, the task is to count the number of elements of the array which are Fibonacci numbers
Example 1:
Input: N = 9, arr[] = {4, 2, 8, 5, 20, 1, 
                              40, 13, 23}
Output: 5
Explanation: Here, Fibonacci series will 
be 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. 
Numbers that are present in array are 
2, 8, 5, 1, 13
Example 2:
Input: N = 4, arr[] = {4, 7, 6, 25} 
Output: 0
Explanation: No Fibonacci number in 
this array.
 
Your Task:
This is a function problem. You don't need to take any input, as it is already accomplished by the driver code. You just need to complete the function checkFib() that takes array arr and integer N as parameters and returns the desired output.
 
Expected Time Complexity: O(N).
Expected Auxiliary Space: O(1).
 
Constraints:
1 ≤ N ≤ 10^{6}

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an orthogonal maze rotated $45$ degrees and drawn with forward and backward slash characters (see below), determine the minimum number of walls that need to be removed to ensure it is possible to escape outside of the maze from every region of the (possibly disconnected) maze.

/\
\/

This maze has only a single region fully enclosed. Removing any wall connects it to the outside.

/\..
\.\.
.\/\
..\/

This maze has two enclosed areas. Two walls need to be removed to connect all regions to the outside.

-----Input-----
The first line has two numbers, $R$ and $C$, giving the number of rows and columns in the maze’s input description. Following this are $R$ lines each with $C$ characters, consisting only of the characters ‘/’, ‘\’, and ‘.’. Both $R$ and $C$ are in the range $1\ldots 1000$.

Define an odd (even) square as one where the sum of the $x$ and $y$ coordinates is odd (even). Either all forward slashes are in the odd squares and all backslashes in the even squares, or vice versa.

-----Output-----
Output on a single line an integer indicating how many walls need to be removed so escape is possible from every region in the maze.

-----Examples-----
Sample Input 1:
2 2
/\
\/
Sample Output 1:
1

Sample Input 2:
4 4
/\..
\.\.
.\/\
..\/
Sample Output 2:
2

Sample Input 3:
2 2
\/
/\
Sample Output 3:
0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given $n$ chips on a number line. The $i$-th chip is placed at the integer coordinate $x_i$. Some chips can have equal coordinates.

You can perform each of the two following types of moves any (possibly, zero) number of times on any chip:

  Move the chip $i$ by $2$ to the left or $2$ to the right for free (i.e. replace the current coordinate $x_i$ with $x_i - 2$ or with $x_i + 2$);  move the chip $i$ by $1$ to the left or $1$ to the right and pay one coin for this move (i.e. replace the current coordinate $x_i$ with $x_i - 1$ or with $x_i + 1$). 

Note that it's allowed to move chips to any integer coordinate, including negative and zero.

Your task is to find the minimum total number of coins required to move all $n$ chips to the same coordinate (i.e. all $x_i$ should be equal after some sequence of moves).


-----Input-----

The first line of the input contains one integer $n$ ($1 \le n \le 100$) — the number of chips.

The second line of the input contains $n$ integers $x_1, x_2, \dots, x_n$ ($1 \le x_i \le 10^9$), where $x_i$ is the coordinate of the $i$-th chip.


-----Output-----

Print one integer — the minimum total number of coins required to move all $n$ chips to the same coordinate.


-----Examples-----
Input
3
1 2 3

Output
1

Input
5
2 2 2 3 3

Output
2



-----Note-----

In the first example you need to move the first chip by $2$ to the right and the second chip by $1$ to the right or move the third chip by $2$ to the left and the second chip by $1$ to the left so the answer is $1$.

In the second example you need to move two chips with coordinate $3$ by $1$ to the left so the answer is $2$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a circular linked list, your task is to complete the method printList() that prints the linked list.
Input:
The printList function takes a single argument as input the reference pointer to the head of the linked list.
There are multiple test cases and for each test, the function will be called separately. 
Output: You just need to print the LinkedList in the same line and the next line will be added by the Driver Code.
Example:
Input:
2
7
374 363 171 497 282 306 426
2
162 231
Output:
426 306 282 497 171 363 374
231 162
Note : Input items are inserted at the front of linked list that is why output is in reverse order.
Constraints:
1<=T<=50
1<=N<=50

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a string str consisting of digits, one may group these digits into sub-groups while maintaining their original order.
The task is to count number of groupings such that for every sub-group except the last one, sum of digits in a sub-group is less than or equal to sum of the digits in the sub-group immediately on its right.
For example, a valid grouping of digits of number 1119 is (1-11-9). Sum of digits in first subgroup is 1, next subgroup is 2, and last subgroup is 9. Sum of every subgroup is less than or equal to its immediate right.
 
Example 1: 
Input: str = "1119"
Output: 7
Explanation: [1-119], [1-1-19], [1-11-9], 
[1-1-1-9], [11-19], [111-9] and [1119] 
are seven sub-groups.
Example 2:
Input: str = "12"
Output: 2
Explanation: [1-2] and [12] are two sub-groups.
 
Your Task:
You don't need to read or print anything. Your task is to complete the function TotalCount() which takes the string str as input parameter and returns total possible groupings.
Expected Time Complexity: O(N * N ) where N is length of string.
Expected Space Complexity: O(N * N)
 
Constraints:
1 <= length of string <= 100

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The chef is trying to decode some pattern problems, Chef wants your help to code it. Chef has one number K to form a new pattern. Help the chef to code this pattern problem.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow. 
- Each test case contains a single line of input, one integer $K$. 

-----Output:-----
For each test case, output as the pattern.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq K \leq 100$

-----Sample Input:-----
4
1
2
3
4

-----Sample Output:-----
0
01
10
012
101
210
0123
1012
2101
3210

-----EXPLANATION:-----
No need, else pattern can be decode easily.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Ravi is very tensed nowadays because of the design project. He has not even decided the topic yet. Micro feels very bad for Ravi, so to help Ravi take his mind off from design project for sometime he gave him a problem. He gave him two strings S and P. Now Ravi has to tell if S can be converted to P by deleting some characters of S.

Input:
First line of input consists of T the number of test cases.
Each test case contain two line. First line consists of string S and second consists of string P.

Output:
For each test case print, in a new line, "YES" (without quotes) if string S can be converted to P otherwise output "NO" (without quotes).

Constraints:
1 ≤ T ≤ 100 
1 ≤ |S| ≤ 10000 
1 ≤ |P| ≤ 10000 
Strings S and P are made of lower case letters only.

SAMPLE INPUT
2
abcde
ade
abc
pe

SAMPLE OUTPUT
YES
NO

Explanation

In first test case string "abcde" can be converted to string "ade" by deleting characters "b" and "c". So answer is YES.
In second case "abc" can not be converted to "pe" so answer is NO.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are n games in a football tournament. Three teams are participating in it. Currently k games had already been played. 

You are an avid football fan, but recently you missed the whole k games. Fortunately, you remember a guess of your friend for these k games. Your friend did not tell exact number of wins of each team, instead he thought that absolute difference between number of wins of first and second team will be d_1 and that of between second and third team will be d_2.

You don't want any of team win the tournament, that is each team should have the same number of wins after n games. That's why you want to know: does there exist a valid tournament satisfying the friend's guess such that no team will win this tournament?

Note that outcome of a match can not be a draw, it has to be either win or loss.


-----Input-----

The first line of the input contains a single integer corresponding to number of test cases t (1 ≤ t ≤ 10^5).

Each of the next t lines will contain four space-separated integers n, k, d_1, d_2 (1 ≤ n ≤ 10^12; 0 ≤ k ≤ n; 0 ≤ d_1, d_2 ≤ k) — data for the current test case.


-----Output-----

For each test case, output a single line containing either "yes" if it is possible to have no winner of tournament, or "no" otherwise (without quotes).


-----Examples-----
Input
5
3 0 0 0
3 3 0 0
6 4 1 0
6 3 3 0
3 3 3 2

Output
yes
yes
yes
no
no



-----Note-----

Sample 1. There has not been any match up to now (k = 0, d_1 = 0, d_2 = 0). If there will be three matches (1-2, 2-3, 3-1) and each team wins once, then at the end each team will have 1 win.

Sample 2. You missed all the games (k = 3). As d_1 = 0 and d_2 = 0, and there is a way to play three games with no winner of tournament (described in the previous sample), the answer is "yes".

Sample 3. You missed 4 matches, and d_1 = 1, d_2 = 0. These four matches can be: 1-2 (win 2), 1-3 (win 3), 1-2 (win 1), 1-3 (win 1). Currently the first team has 2 wins, the second team has 1 win, the third team has 1 win. Two remaining matches can be: 1-2 (win 2), 1-3 (win 3). In the end all the teams have equal number of wins (2 wins).

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).

Let R=10^{10^{10^{10}}}. Ringo performs the following operation:

* Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.



For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.

Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:

* Pick two real numbers x and y independently according to uniform distribution on [-R,R].
* If x^2+y^2\leq R^2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.

Constraints

* 2 \leq N \leq 100
* |x_i|,|y_i| \leq 10^6(1\leq i\leq N)
* All given points are pairwise distinct.
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1
:
x_N y_N


Output

Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.

The output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.

Examples

Input

2
0 0
1 1


Output

0.5
0.5


Input

5
0 0
2 8
4 5
2 6
3 10


Output

0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The only difference between easy and hard versions is constraints.

Nauuo is a girl who loves random picture websites.

One day she made a random picture website by herself which includes $n$ pictures.

When Nauuo visits the website, she sees exactly one picture. The website does not display each picture with equal probability. The $i$-th picture has a non-negative weight $w_i$, and the probability of the $i$-th picture being displayed is $\frac{w_i}{\sum_{j=1}^nw_j}$. That is to say, the probability of a picture to be displayed is proportional to its weight.

However, Nauuo discovered that some pictures she does not like were displayed too often. 

To solve this problem, she came up with a great idea: when she saw a picture she likes, she would add $1$ to its weight; otherwise, she would subtract $1$ from its weight.

Nauuo will visit the website $m$ times. She wants to know the expected weight of each picture after all the $m$ visits modulo $998244353$. Can you help her?

The expected weight of the $i$-th picture can be denoted by $\frac {q_i} {p_i}$ where $\gcd(p_i,q_i)=1$, you need to print an integer $r_i$ satisfying $0\le r_i<998244353$ and $r_i\cdot p_i\equiv q_i\pmod{998244353}$. It can be proved that such $r_i$ exists and is unique.


-----Input-----

The first line contains two integers $n$ and $m$ ($1\le n\le 2\cdot 10^5$, $1\le m\le 3000$) — the number of pictures and the number of visits to the website.

The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ ($a_i$ is either $0$ or $1$) — if $a_i=0$ , Nauuo does not like the $i$-th picture; otherwise Nauuo likes the $i$-th picture. It is guaranteed that there is at least one picture which Nauuo likes.

The third line contains $n$ positive integers $w_1,w_2,\ldots,w_n$ ($w_i \geq 1$) — the initial weights of the pictures. It is guaranteed that the sum of all the initial weights does not exceed $998244352-m$.


-----Output-----

The output contains $n$ integers $r_1,r_2,\ldots,r_n$ — the expected weights modulo $998244353$.


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

Output
332748119
332748119

Input
1 2
1
1

Output
3

Input
3 3
0 1 1
4 3 5

Output
160955686
185138929
974061117



-----Note-----

In the first example, if the only visit shows the first picture with a probability of $\frac 2 3$, the final weights are $(1,1)$; if the only visit shows the second picture with a probability of $\frac1 3$, the final weights are $(2,2)$.

So, both expected weights are $\frac2 3\cdot 1+\frac 1 3\cdot 2=\frac4 3$ .

Because $332748119\cdot 3\equiv 4\pmod{998244353}$, you need to print $332748119$ instead of $\frac4 3$ or $1.3333333333$.

In the second example, there is only one picture which Nauuo likes, so every time Nauuo visits the website, $w_1$ will be increased by $1$.

So, the expected weight is $1+2=3$.

Nauuo is very naughty so she didn't give you any hint of the third example.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Little Artem and Presents

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Little Artem got *n* stones on his birthday and now wants to give some of them to Masha. He knows that Masha cares more about the fact of receiving the present, rather than the value of that present, so he wants to give her stones as many times as possible. However, Masha remembers the last present she received, so Artem can't give her the same number of stones twice in a row. For example, he can give her 3 stones, then 1 stone, then again 3 stones, but he can't give her 3 stones and then again 3 stones right after that.

How many times can Artem give presents to Masha?

Input Specification:
The only line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=109) — number of stones Artem received on his birthday.

Output Specification:
Print the maximum possible number of times Artem can give presents to Masha.

Demo Input:
['1\n', '2\n', '3\n', '4\n']

Demo Output:
['1\n', '1\n', '2\n', '3\n']

Note:
In the first sample, Artem can only give 1 stone to Masha.

In the second sample, Atrem can give Masha 1 or 2 stones, though he can't give her 1 stone two times.

In the third sample, Atrem can first give Masha 2 stones, a then 1 more stone.

In the fourth sample, Atrem can first give Masha 1 stone, then 2 stones, and finally 1 stone again.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.