message stringlengths 2 44.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 276 109k | cluster float64 23 23 | __index_level_0__ int64 552 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points on a plane. Write a program which will find the sum of squares of distances between all pairs of points.
Input
The first line of input contains one integer number N (1 β€ N β€ 100 000) β the number of points. Each of the following N lines contain two integer numbers X and Y ( - 10 000 β€ X, Y β€ 10 000) β the coordinates of points. Two or more points may coincide.
Output
The only line of output should contain the required sum of squares of distances between all pairs of points.
Examples
Input
4
1 1
-1 -1
1 -1
-1 1
Output
32
Submitted Solution:
```
import math
t = int(input())
a = []
for i in range(t):
x,y = map(int, input().split())
a.append([x,y])
count = 0
for i in range(len(a)):
for j in range(i+1,len(a)):
s = math.sqrt((a[i][0] - a[j][0])**2 + (a[i][1] - a[j][1])**2)
print(a[i],a[j])
count += s**2
print(count)
``` | instruction | 0 | 39,224 | 23 | 78,448 |
No | output | 1 | 39,224 | 23 | 78,449 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points on a plane. Write a program which will find the sum of squares of distances between all pairs of points.
Input
The first line of input contains one integer number N (1 β€ N β€ 100 000) β the number of points. Each of the following N lines contain two integer numbers X and Y ( - 10 000 β€ X, Y β€ 10 000) β the coordinates of points. Two or more points may coincide.
Output
The only line of output should contain the required sum of squares of distances between all pairs of points.
Examples
Input
4
1 1
-1 -1
1 -1
-1 1
Output
32
Submitted Solution:
```
n = int(input())
r = 0
x = [0]*n
y = [0]*n
for i in range(n):
a, b = map(int, input().split())
r += n*(a**2+b**2)
x[i] = a
y[i] = b
x_sum = sum(x[1:])
y_sum = sum(y[1:])
#
for i in range(n-1):
r -= 2*x_sum*y_sum
x_sum -= x[i+1]
y_sum -= y[i+1]
print(r)
``` | instruction | 0 | 39,225 | 23 | 78,450 |
No | output | 1 | 39,225 | 23 | 78,451 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N points on a plane. Write a program which will find the sum of squares of distances between all pairs of points.
Input
The first line of input contains one integer number N (1 β€ N β€ 100 000) β the number of points. Each of the following N lines contain two integer numbers X and Y ( - 10 000 β€ X, Y β€ 10 000) β the coordinates of points. Two or more points may coincide.
Output
The only line of output should contain the required sum of squares of distances between all pairs of points.
Examples
Input
4
1 1
-1 -1
1 -1
-1 1
Output
32
Submitted Solution:
```
import math
t = int(input())
a = []
for i in range(t):
x,y = map(int, input().split())
a.append([x,y])
count = 0
for i in range(len(a)):
for j in range(i+1,len(a)):
s = math.sqrt((a[i][0] - a[j][0])**2 + (a[i][1] - a[j][1])**2)
count += s**2
print(count)
``` | instruction | 0 | 39,226 | 23 | 78,452 |
No | output | 1 | 39,226 | 23 | 78,453 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>. | instruction | 0 | 39,227 | 23 | 78,454 |
Tags: geometry, math
Correct Solution:
```
from math import sqrt
n, h = map(int, input().split(' '))
for i in range(1, n):
r = h*sqrt(i/n)
print(str(r), end=" ")
``` | output | 1 | 39,227 | 23 | 78,455 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>. | instruction | 0 | 39,228 | 23 | 78,456 |
Tags: geometry, math
Correct Solution:
```
import math
a = input()
x = [int(i) for i in a.split()]
number = x[0]
height = x[1]
output = ""
for i in range(1, number):
if(number == 1):
print(math.sqrt(i/number) * height)
else:
output = output + str(math.sqrt(i/number) * height) + " "
print(output)
``` | output | 1 | 39,228 | 23 | 78,457 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>. | instruction | 0 | 39,229 | 23 | 78,458 |
Tags: geometry, math
Correct Solution:
```
#794B
from math import sqrt
[n,h] = list(map(int,input().split()))
for i in range(1,n):
print(sqrt(i/n)*h,end=' ')
``` | output | 1 | 39,229 | 23 | 78,459 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>. | instruction | 0 | 39,230 | 23 | 78,460 |
Tags: geometry, math
Correct Solution:
```
# 764B
# Cutting Carrot
import math
fstline = list(map(float,input().split(' ')))
n, h, i, ans = fstline[0], fstline[1], 1, ''
while i < n:
ans+=str(math.sqrt(i/n)*h)+' '
i+=1
print(ans[:-1])
``` | output | 1 | 39,230 | 23 | 78,461 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>. | instruction | 0 | 39,231 | 23 | 78,462 |
Tags: geometry, math
Correct Solution:
```
import math
n,h=map(int ,input().split())
a=1/2*(h)
ans=[]
for i in range(1,n):
ans.append(h*math.sqrt(i/n))
print(*ans)
``` | output | 1 | 39,231 | 23 | 78,463 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>. | instruction | 0 | 39,232 | 23 | 78,464 |
Tags: geometry, math
Correct Solution:
```
import math
n,h=map(int,input().split())
for i in range(1,n):
print(h*math.sqrt(i/n),end=" ")
``` | output | 1 | 39,232 | 23 | 78,465 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>. | instruction | 0 | 39,233 | 23 | 78,466 |
Tags: geometry, math
Correct Solution:
```
n, h = map(int, input().split())
for i in range(1,n):
res = (i / n)**(1/2) * h
print(res, end=' ')
``` | output | 1 | 39,233 | 23 | 78,467 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>. | instruction | 0 | 39,234 | 23 | 78,468 |
Tags: geometry, math
Correct Solution:
```
import sys
import os
import math
import re
n,h = map(int,input().split())
for i in range(1,n):
print(str(h*math.sqrt(i/n)) + " ",end = "")
print()
``` | output | 1 | 39,234 | 23 | 78,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.
Submitted Solution:
```
from sys import stdin,stdout
n,h = [int (x) for x in stdin.readline().split()]
for i in range(1,n):
res = ((i/n)**.5)*h
stdout.write(str(res))
if i < n-1:
stdout.write(' ')
stdout.write('\n')
``` | instruction | 0 | 39,235 | 23 | 78,470 |
Yes | output | 1 | 39,235 | 23 | 78,471 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.
Submitted Solution:
```
import math
n, h = [int(i) for i in input().split()]
pp = h / 2
przydzial = pp / n
z = math.sqrt(2*przydzial*h)
for i in range(n-1):
print(math.sqrt(2*przydzial*(i+1)*h), end=" ")
``` | instruction | 0 | 39,236 | 23 | 78,472 |
Yes | output | 1 | 39,236 | 23 | 78,473 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.
Submitted Solution:
```
n, H = (int(x) for x in input().split())
list_of_h = [H * ((i / n) ** 0.5) for i in range(1, n)]
print(*list_of_h)
``` | instruction | 0 | 39,237 | 23 | 78,474 |
Yes | output | 1 | 39,237 | 23 | 78,475 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.
Submitted Solution:
```
import math
n, h = map(int, input().split())
for i in range(1, n):
print(2 * h / 2 * i / (math.sqrt(i / n) * n), end=' ')
``` | instruction | 0 | 39,238 | 23 | 78,476 |
Yes | output | 1 | 39,238 | 23 | 78,477 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.
Submitted Solution:
```
import math
n, h = map(int, input().split())
prev = 1/n
pprev = prev
print(h*math.sqrt(prev), end=' ')
for x in range(n - 2):
curr = pprev + prev
print(h*math.sqrt(curr), end=' ')
pprev = prev
prev = curr
``` | instruction | 0 | 39,239 | 23 | 78,478 |
No | output | 1 | 39,239 | 23 | 78,479 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.
Submitted Solution:
```
n, h = [int(x) for x in input().split()]
def tarea(v):
return (v**2)/(2*h)
def area(prev_h, curr_h):
return tarea(curr_h) - tarea(prev_h)
P = h/2
Pn = P/n
prev_cut = 0
for i in range(n - 1):
lo = prev_cut
hi = h
while lo < hi:
mid = (hi + lo)/2
a = area(prev_cut, mid)
if abs(a - Pn) < 1e-6:
prev_cut = mid
break
elif a > Pn:
hi = mid
else:
lo = mid
print(prev_cut)
``` | instruction | 0 | 39,240 | 23 | 78,480 |
No | output | 1 | 39,240 | 23 | 78,481 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.
Submitted Solution:
```
import math
n,h=map(int,input().split())
x=math.acos(0.5/h)
L=h*math.tan(x)
for i in range(1,n):
print(math.sqrt((L*i)/(2*n)))
``` | instruction | 0 | 39,241 | 23 | 78,482 |
No | output | 1 | 39,241 | 23 | 78,483 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.
Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?
<image> Illustration to the first example.
Input
The first and only line of input contains two space-separated integers, n and h (2 β€ n β€ 1000, 1 β€ h β€ 105).
Output
The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold.
Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.
Examples
Input
3 2
Output
1.154700538379 1.632993161855
Input
2 100000
Output
70710.678118654752
Note
Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.
Submitted Solution:
```
n, h = map(int, input().split())
eps = (10 ** -7)
cur = h
s = h / (2 * n)
h = [h]
def sz(a):
return (h[0] - a) / h[0]
def area(a,b):
return (sz(a) + sz(b)) * abs(a - b) * (1 / 2)
def find(cur):
l, r = 0, cur
while r - l > eps:
m = (l + r) / 2
if area(cur, m) > s:
l = m
else:
r = m
print(h[0] - r)
return r
for i in range(n - 1):
cur = find(cur)
``` | instruction | 0 | 39,242 | 23 | 78,484 |
No | output | 1 | 39,242 | 23 | 78,485 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8 | instruction | 0 | 39,499 | 23 | 78,998 |
"Correct Solution:
```
import fractions
a,b,c,d=map(int,input().split())
c=abs(c-a)
d=abs(d-b)
g=fractions.gcd(max(c,d),min(c,d))
j=int(c/g)
k=int(d/g)
print((j+k-1)*g)
``` | output | 1 | 39,499 | 23 | 78,999 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8 | instruction | 0 | 39,500 | 23 | 79,000 |
"Correct Solution:
```
def gcd(x,y):
if x%y==0:
return y
while x%y>0:
x,y=y,x%y
return y
a,b,c,d=map(int,input().split())
x,y=abs(a-c),abs(b-d)
g=gcd(x,y)
print(g*(x//g+y//g-1))
``` | output | 1 | 39,500 | 23 | 79,001 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8 | instruction | 0 | 39,501 | 23 | 79,002 |
"Correct Solution:
```
import fractions
x1,y1,x2,y2 = map(int,input().split())
if x1 == x2 or y1 == y2:
print(0)
exit()
dx,dy = abs(x1-x2),abs(y1-y2)
g = fractions.gcd(dx,dy)
print(g * (dx//g + dy//g - 1))
``` | output | 1 | 39,501 | 23 | 79,003 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8 | instruction | 0 | 39,502 | 23 | 79,004 |
"Correct Solution:
```
from fractions import gcd
import math
a, b, c, d = [int(item) for item in input().split()]
a = abs(a - c)
b = abs(b - d)
if a > b:
a, b = b, a
g = gcd(a, b)
a //= g; b //= g
print((a + b - 1) * g)
``` | output | 1 | 39,502 | 23 | 79,005 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8 | instruction | 0 | 39,503 | 23 | 79,006 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)
a, b, c, d = map(int, input().split())
if a == c or b == d:
print(0)
sys.exit(0)
def gcd(a, b):
if b == 0:
return a
else:
return gcd(b, a % b)
x = abs(a - c)
y = abs(b - d)
_gcd = gcd(x, y)
x2 = x // _gcd
y2 = y // _gcd
import math
print((x2 + y2 - 1) * _gcd)
``` | output | 1 | 39,503 | 23 | 79,007 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8 | instruction | 0 | 39,504 | 23 | 79,008 |
"Correct Solution:
```
a,b,c,d=map(int,input().split())
gcd=lambda a,b:gcd(b,a%b)if a%b else b
def ζ°ε¦γ―ζεΌ·δΉ(a,b):
q=gcd(a,b)
return q*((a//q)+(b//q-1))
print(ζ°ε¦γ―ζεΌ·δΉ(abs(a-c),abs(b-d)))
``` | output | 1 | 39,504 | 23 | 79,009 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8 | instruction | 0 | 39,505 | 23 | 79,010 |
"Correct Solution:
```
import fractions
if __name__ == "__main__":
A, B, C, D = map(int, input().split())
A -= C
B -= D
W = abs(A)
H = abs(B)
if W == 0 or H == 0:
print(0)
exit()
res = W + H - 1
g = fractions.gcd(W, H)
print(res - g + 1)
``` | output | 1 | 39,505 | 23 | 79,011 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8 | instruction | 0 | 39,506 | 23 | 79,012 |
"Correct Solution:
```
def gcd(a,b):
if b==0:return a
return gcd(b,a%b)
a,b,c,d=map(int,input().split())
c=abs(c-a)
d=abs(d-b)
g=gcd(max(c,d),min(c,d))
j=int(c/g)
k=int(d/g)
print((j+k-1)*g)
``` | output | 1 | 39,506 | 23 | 79,013 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8
Submitted Solution:
```
a,b,c,d = (int(i) for i in input().split())
def gcd(x,y):
if x%y==0: return y
else: return gcd(y,x%y)
if a==c or b==d: ans = 0
else:
n = gcd(abs(a-c),abs(b-d))
e,f = abs(a-c)//n,abs(b-d)//n
ans = (e+f-1)*n
print(ans)
``` | instruction | 0 | 39,507 | 23 | 79,014 |
Yes | output | 1 | 39,507 | 23 | 79,015 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8
Submitted Solution:
```
import fractions
a,b,c,d=map(int,input().split())
c=abs(c-a)
d=abs(d-b)
g=fractions.gcd(c,d)
j=int(c/g)
k=int(d/g)
print((j+k-1)*g)
``` | instruction | 0 | 39,508 | 23 | 79,016 |
Yes | output | 1 | 39,508 | 23 | 79,017 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8
Submitted Solution:
```
from fractions import gcd
a, b, c, d = map(int, input().split())
ac = abs(a - c)
bd = abs(b - d)
if ac == bd:
ans = ac
elif ac == 0 or bd == 0:
ans = 0
else:
ans = ac + bd - gcd(ac, bd)
print(ans)
``` | instruction | 0 | 39,509 | 23 | 79,018 |
Yes | output | 1 | 39,509 | 23 | 79,019 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8
Submitted Solution:
```
import fractions
def main():
a,b,c,d = map(int,input().split())
a,c = min(a,c),max(a,c)
b,d = min(b,d),max(b,d)
c -= a
a = 0
d -= b
b = 0
if a==c or b==d:
return 0
g = fractions.gcd(c,d)
c//=g
d//=g
ct = c+d-1
return g*ct
if __name__ == '__main__':
print(main())
``` | instruction | 0 | 39,510 | 23 | 79,020 |
Yes | output | 1 | 39,510 | 23 | 79,021 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8
Submitted Solution:
```
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)
a, b, c, d = map(int, input().split())
if a == c or b == d:
print(0)
sys.exit(0)
def gcd(a, b):
if b == 0:
return a
else:
return gcd(b, a % b)
x = abs(a - c)
y = abs(b - d)
_gcd = gcd(x, y)
x2 = x // _gcd
y2 = y // _gcd
import math
print(x2, y2)
print((math.ceil(y2 / x2) * x2) * _gcd)
``` | instruction | 0 | 39,511 | 23 | 79,022 |
No | output | 1 | 39,511 | 23 | 79,023 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8
Submitted Solution:
```
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)
a, b, c, d = map(int, input().split())
def gcd(a, b):
if b == 0:
return a
else:
return gcd(b, a % b)
x = abs(a - c)
y = abs(b - d)
_gcd = gcd(x, y)
x2 = x // _gcd
y2 = y // _gcd
import math
print((math.ceil(y2 / x2) * x2) * _gcd)
``` | instruction | 0 | 39,512 | 23 | 79,024 |
No | output | 1 | 39,512 | 23 | 79,025 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8
Submitted Solution:
```
def gcd(a,b):
if b==0:return a
return gcd(b,a%b)
a,b,c,d=map(int,input().split())
c-=a
d-=b
g=gcd(max(c,d),min(c,d))
j=int(c/g)
k=int(d/g)
print((j+k-1)*g)
``` | instruction | 0 | 39,513 | 23 | 79,026 |
No | output | 1 | 39,513 | 23 | 79,027 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is drawing a segment on grid paper.
From a certain square, a square that is x squares to the right and y squares above, is denoted as square (x, y).
When Takahashi draws a segment connecting the lower left corner of square (A, B) and the lower left corner of square (C, D), find the number of the squares crossed by the segment.
Here, the segment is said to cross a square if the segment has non-empty intersection with the region within the square, excluding the boundary.
Constraints
* 1 \leq A, B, C, D \leq 10^9
* At least one of A \neq C and B \neq D holds.
Input
The input is given from Standard Input in the following format:
A B C D
Output
Print the number of the squares crossed by the segment.
Examples
Input
1 1 3 4
Output
4
Input
2 3 10 7
Output
8
Submitted Solution:
```
from fractions import gcd
import math
a, b, c, d = [int(item) for item in input().split()]
a = abs(a - c)
b = abs(b - d)
if a > b:
a, b = b, a
g = gcd(a, b)
a //= g; b //= g
print(math.ceil(b / a) * a * g)
``` | instruction | 0 | 39,514 | 23 | 79,028 |
No | output | 1 | 39,514 | 23 | 79,029 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n segments on a number line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.
The intersection of a sequence of segments is such a maximal set of points (not necesserily having integer coordinates) that each point lies within every segment from the sequence. If the resulting set isn't empty, then it always forms some continuous segment. The length of the intersection is the length of the resulting segment or 0 in case the intersection is an empty set.
For example, the intersection of segments [1;5] and [3;10] is [3;5] (length 2), the intersection of segments [1;5] and [5;7] is [5;5] (length 0) and the intersection of segments [1;5] and [6;6] is an empty set (length 0).
Your task is to remove exactly one segment from the given sequence in such a way that the intersection of the remaining (n - 1) segments has the maximal possible length.
Input
The first line contains a single integer n (2 β€ n β€ 3 β
10^5) β the number of segments in the sequence.
Each of the next n lines contains two integers l_i and r_i (0 β€ l_i β€ r_i β€ 10^9) β the description of the i-th segment.
Output
Print a single integer β the maximal possible length of the intersection of (n - 1) remaining segments after you remove exactly one segment from the sequence.
Examples
Input
4
1 3
2 6
0 4
3 3
Output
1
Input
5
2 6
1 3
0 4
1 20
0 4
Output
2
Input
3
4 5
1 2
9 20
Output
0
Input
2
3 10
1 5
Output
7
Note
In the first example you should remove the segment [3;3], the intersection will become [2;3] (length 1). Removing any other segment will result in the intersection [3;3] (length 0).
In the second example you should remove the segment [1;3] or segment [2;6], the intersection will become [2;4] (length 2) or [1;3] (length 2), respectively. Removing any other segment will result in the intersection [2;3] (length 1).
In the third example the intersection will become an empty set no matter the segment you remove.
In the fourth example you will get the intersection [3;10] (length 7) if you remove the segment [1;5] or the intersection [1;5] (length 4) if you remove the segment [3;10].
Submitted Solution:
```
n = int(input())
if n != 1 and n != 2:
max12l = [0, 0]
min12r = [10 ** 10, 10 ** 10]
badcl = dict()
badcr = dict()
for u in range(n):
l, r = map(int, input().split())
if l > min(max12l):
max12l[max12l.index(min(max12l))] = l
if r < max(min12r):
min12r[min12r.index(max(min12r))] = r
if r not in badcr:
badcr[r] = set()
badcr[r].add(l)
lol = 0
kek = 0
a = min(max12l)
b = max(max12l)
c = min(min12r)
d = max(min12r)
interes = [0]
if b in badcr[c]:
interes.append(d - a)
if len(badcr[c]) != 1 or b not in badcr[c]:
interes.append(d - b)
interes.append(c - a)
print(max(interes))
elif n == 2:
l1, r1 = map(int, input().split())
l12, r2 = map(int, input().split())
print(max(r1 - l1, r2 - l12))
else:
print(0)
``` | instruction | 0 | 39,608 | 23 | 79,216 |
Yes | output | 1 | 39,608 | 23 | 79,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n segments on a number line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.
The intersection of a sequence of segments is such a maximal set of points (not necesserily having integer coordinates) that each point lies within every segment from the sequence. If the resulting set isn't empty, then it always forms some continuous segment. The length of the intersection is the length of the resulting segment or 0 in case the intersection is an empty set.
For example, the intersection of segments [1;5] and [3;10] is [3;5] (length 2), the intersection of segments [1;5] and [5;7] is [5;5] (length 0) and the intersection of segments [1;5] and [6;6] is an empty set (length 0).
Your task is to remove exactly one segment from the given sequence in such a way that the intersection of the remaining (n - 1) segments has the maximal possible length.
Input
The first line contains a single integer n (2 β€ n β€ 3 β
10^5) β the number of segments in the sequence.
Each of the next n lines contains two integers l_i and r_i (0 β€ l_i β€ r_i β€ 10^9) β the description of the i-th segment.
Output
Print a single integer β the maximal possible length of the intersection of (n - 1) remaining segments after you remove exactly one segment from the sequence.
Examples
Input
4
1 3
2 6
0 4
3 3
Output
1
Input
5
2 6
1 3
0 4
1 20
0 4
Output
2
Input
3
4 5
1 2
9 20
Output
0
Input
2
3 10
1 5
Output
7
Note
In the first example you should remove the segment [3;3], the intersection will become [2;3] (length 1). Removing any other segment will result in the intersection [3;3] (length 0).
In the second example you should remove the segment [1;3] or segment [2;6], the intersection will become [2;4] (length 2) or [1;3] (length 2), respectively. Removing any other segment will result in the intersection [2;3] (length 1).
In the third example the intersection will become an empty set no matter the segment you remove.
In the fourth example you will get the intersection [3;10] (length 7) if you remove the segment [1;5] or the intersection [1;5] (length 4) if you remove the segment [3;10].
Submitted Solution:
```
n = int(input())
l = [0] * n
r = [0] * n
for i in range(n):
l[i], r[i] = map(int, input().split())
one = l.index(max(l))
two = r.index(min(r))
if one == 0:
f = min(r[1:]) - max(l[1:])
elif one == n - 1:
f = min(r[:n - 1]) - max(l[:n - 1])
else:
f = min(min(r[:one]), min(r[one + 1:])) - max(max(l[:one]), max(l[one + 1:]))
if two == 0:
s = min(r[1:]) - max(l[1:])
elif two == n - 1:
s = min(r[:n - 1]) - max(l[:n - 1])
else:
s = min(min(r[:two]), min(r[two + 1:])) - max(max(l[:two]), max(l[two + 1:]))
print(max(max(f, s), 0))
``` | instruction | 0 | 39,609 | 23 | 79,218 |
Yes | output | 1 | 39,609 | 23 | 79,219 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n segments on a number line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.
The intersection of a sequence of segments is such a maximal set of points (not necesserily having integer coordinates) that each point lies within every segment from the sequence. If the resulting set isn't empty, then it always forms some continuous segment. The length of the intersection is the length of the resulting segment or 0 in case the intersection is an empty set.
For example, the intersection of segments [1;5] and [3;10] is [3;5] (length 2), the intersection of segments [1;5] and [5;7] is [5;5] (length 0) and the intersection of segments [1;5] and [6;6] is an empty set (length 0).
Your task is to remove exactly one segment from the given sequence in such a way that the intersection of the remaining (n - 1) segments has the maximal possible length.
Input
The first line contains a single integer n (2 β€ n β€ 3 β
10^5) β the number of segments in the sequence.
Each of the next n lines contains two integers l_i and r_i (0 β€ l_i β€ r_i β€ 10^9) β the description of the i-th segment.
Output
Print a single integer β the maximal possible length of the intersection of (n - 1) remaining segments after you remove exactly one segment from the sequence.
Examples
Input
4
1 3
2 6
0 4
3 3
Output
1
Input
5
2 6
1 3
0 4
1 20
0 4
Output
2
Input
3
4 5
1 2
9 20
Output
0
Input
2
3 10
1 5
Output
7
Note
In the first example you should remove the segment [3;3], the intersection will become [2;3] (length 1). Removing any other segment will result in the intersection [3;3] (length 0).
In the second example you should remove the segment [1;3] or segment [2;6], the intersection will become [2;4] (length 2) or [1;3] (length 2), respectively. Removing any other segment will result in the intersection [2;3] (length 1).
In the third example the intersection will become an empty set no matter the segment you remove.
In the fourth example you will get the intersection [3;10] (length 7) if you remove the segment [1;5] or the intersection [1;5] (length 4) if you remove the segment [3;10].
Submitted Solution:
```
n=int(input())
s,e=[],[]
a=[]
for i in range(n):
ss,ee=map(int,input().split())
s.append(ss)
e.append(ee)
a.append([ss,ee])
s.sort()
e.sort()
ans=[e[0]-s[n-1]]
sv=s[n-1]
ev=e[0]
for i in range(n):
sv=s[n-1]
ev=e[0]
if a[i][0]==sv:
sv=s[n-2]
if a[i][1]==ev:
ev=e[1]
ans.append(ev-sv)
print(max(0,max(ans)))
``` | instruction | 0 | 39,610 | 23 | 79,220 |
Yes | output | 1 | 39,610 | 23 | 79,221 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n segments on a number line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.
The intersection of a sequence of segments is such a maximal set of points (not necesserily having integer coordinates) that each point lies within every segment from the sequence. If the resulting set isn't empty, then it always forms some continuous segment. The length of the intersection is the length of the resulting segment or 0 in case the intersection is an empty set.
For example, the intersection of segments [1;5] and [3;10] is [3;5] (length 2), the intersection of segments [1;5] and [5;7] is [5;5] (length 0) and the intersection of segments [1;5] and [6;6] is an empty set (length 0).
Your task is to remove exactly one segment from the given sequence in such a way that the intersection of the remaining (n - 1) segments has the maximal possible length.
Input
The first line contains a single integer n (2 β€ n β€ 3 β
10^5) β the number of segments in the sequence.
Each of the next n lines contains two integers l_i and r_i (0 β€ l_i β€ r_i β€ 10^9) β the description of the i-th segment.
Output
Print a single integer β the maximal possible length of the intersection of (n - 1) remaining segments after you remove exactly one segment from the sequence.
Examples
Input
4
1 3
2 6
0 4
3 3
Output
1
Input
5
2 6
1 3
0 4
1 20
0 4
Output
2
Input
3
4 5
1 2
9 20
Output
0
Input
2
3 10
1 5
Output
7
Note
In the first example you should remove the segment [3;3], the intersection will become [2;3] (length 1). Removing any other segment will result in the intersection [3;3] (length 0).
In the second example you should remove the segment [1;3] or segment [2;6], the intersection will become [2;4] (length 2) or [1;3] (length 2), respectively. Removing any other segment will result in the intersection [2;3] (length 1).
In the third example the intersection will become an empty set no matter the segment you remove.
In the fourth example you will get the intersection [3;10] (length 7) if you remove the segment [1;5] or the intersection [1;5] (length 4) if you remove the segment [3;10].
Submitted Solution:
```
n = int(input())
a = [list(map(int, input().split())) + [i] for i in range(n)]
b = a.copy()
max_L_1, max_L_2, min_R_1, min_R_2 = 0, 0, 0, 0
b.sort(reverse=True)
max_L_1, max_L_2 = b[0][2], b[1][2]
b.sort(key=lambda x: x[1])
min_R_1, min_R_2 = b[0][2], b[1][2]
max_l = 0
for i in range(n):
left = a[max_L_1][0] if i != max_L_1 else a[max_L_2][0]
right = a[min_R_1][1] if i != min_R_1 else a[min_R_2][1]
max_l = max(right - left, max_l)
print(max_l)
``` | instruction | 0 | 39,611 | 23 | 79,222 |
Yes | output | 1 | 39,611 | 23 | 79,223 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n segments on a number line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.
The intersection of a sequence of segments is such a maximal set of points (not necesserily having integer coordinates) that each point lies within every segment from the sequence. If the resulting set isn't empty, then it always forms some continuous segment. The length of the intersection is the length of the resulting segment or 0 in case the intersection is an empty set.
For example, the intersection of segments [1;5] and [3;10] is [3;5] (length 2), the intersection of segments [1;5] and [5;7] is [5;5] (length 0) and the intersection of segments [1;5] and [6;6] is an empty set (length 0).
Your task is to remove exactly one segment from the given sequence in such a way that the intersection of the remaining (n - 1) segments has the maximal possible length.
Input
The first line contains a single integer n (2 β€ n β€ 3 β
10^5) β the number of segments in the sequence.
Each of the next n lines contains two integers l_i and r_i (0 β€ l_i β€ r_i β€ 10^9) β the description of the i-th segment.
Output
Print a single integer β the maximal possible length of the intersection of (n - 1) remaining segments after you remove exactly one segment from the sequence.
Examples
Input
4
1 3
2 6
0 4
3 3
Output
1
Input
5
2 6
1 3
0 4
1 20
0 4
Output
2
Input
3
4 5
1 2
9 20
Output
0
Input
2
3 10
1 5
Output
7
Note
In the first example you should remove the segment [3;3], the intersection will become [2;3] (length 1). Removing any other segment will result in the intersection [3;3] (length 0).
In the second example you should remove the segment [1;3] or segment [2;6], the intersection will become [2;4] (length 2) or [1;3] (length 2), respectively. Removing any other segment will result in the intersection [2;3] (length 1).
In the third example the intersection will become an empty set no matter the segment you remove.
In the fourth example you will get the intersection [3;10] (length 7) if you remove the segment [1;5] or the intersection [1;5] (length 4) if you remove the segment [3;10].
Submitted Solution:
```
a = []
for _ in range(int(input())):
a.append(list(map(int, input().split())))
a.sort(key = lambda i : i[1] - i[0], reverse = 1)
l, r = -1, 10**10
possible = []
for i in a:
l, r = max(l, i[0]), min(r, i[1])
possible.append([l, r])
possible = possible[::-1]
if possible[1][1] - possible[1][0] >= 0:
print(possible[1][1] - possible[1][0])
else:
print(0)
``` | instruction | 0 | 39,612 | 23 | 79,224 |
No | output | 1 | 39,612 | 23 | 79,225 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n segments on a number line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.
The intersection of a sequence of segments is such a maximal set of points (not necesserily having integer coordinates) that each point lies within every segment from the sequence. If the resulting set isn't empty, then it always forms some continuous segment. The length of the intersection is the length of the resulting segment or 0 in case the intersection is an empty set.
For example, the intersection of segments [1;5] and [3;10] is [3;5] (length 2), the intersection of segments [1;5] and [5;7] is [5;5] (length 0) and the intersection of segments [1;5] and [6;6] is an empty set (length 0).
Your task is to remove exactly one segment from the given sequence in such a way that the intersection of the remaining (n - 1) segments has the maximal possible length.
Input
The first line contains a single integer n (2 β€ n β€ 3 β
10^5) β the number of segments in the sequence.
Each of the next n lines contains two integers l_i and r_i (0 β€ l_i β€ r_i β€ 10^9) β the description of the i-th segment.
Output
Print a single integer β the maximal possible length of the intersection of (n - 1) remaining segments after you remove exactly one segment from the sequence.
Examples
Input
4
1 3
2 6
0 4
3 3
Output
1
Input
5
2 6
1 3
0 4
1 20
0 4
Output
2
Input
3
4 5
1 2
9 20
Output
0
Input
2
3 10
1 5
Output
7
Note
In the first example you should remove the segment [3;3], the intersection will become [2;3] (length 1). Removing any other segment will result in the intersection [3;3] (length 0).
In the second example you should remove the segment [1;3] or segment [2;6], the intersection will become [2;4] (length 2) or [1;3] (length 2), respectively. Removing any other segment will result in the intersection [2;3] (length 1).
In the third example the intersection will become an empty set no matter the segment you remove.
In the fourth example you will get the intersection [3;10] (length 7) if you remove the segment [1;5] or the intersection [1;5] (length 4) if you remove the segment [3;10].
Submitted Solution:
```
def read_line():
return [int(w) for w in input().strip().split(' ')]
def intersect(a, b):
if a is None and b is None:
return None
if a is None:
return b
if b is None:
return a
start = max(a[0], b[0])
end = min(a[1], b[1])
if start <= end:
return [start, end]
return None
def line_len(line):
if line is None:
return 0
return line[1] - line[0]
def main():
n = int(input().strip())
lines = []
for i in range(n):
lines.append(read_line())
if n <= 1:
print(0)
return
# left intersect
V = []
for i in range(n):
if i == 0:
V.append(lines[i])
else:
V.append(intersect(V[i-1], lines[i]))
# right intersect
W = []
for i in range(n):
if i == 0:
W.append(lines[n - i - 1])
else:
W.append(intersect(W[i-1], lines[n-i-1]))
W.reverse()
M = 0
for i in range(n):
if i == 0:
M = max(M, line_len(W[i+1]))
elif i == n - 1:
M = max(M, line_len(V[i-1]))
else:
M = max(M, line_len(intersect(V[i-1], W[i+1])))
print(M)
if __name__ == '__main__':
main()
``` | instruction | 0 | 39,613 | 23 | 79,226 |
No | output | 1 | 39,613 | 23 | 79,227 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n segments on a number line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.
The intersection of a sequence of segments is such a maximal set of points (not necesserily having integer coordinates) that each point lies within every segment from the sequence. If the resulting set isn't empty, then it always forms some continuous segment. The length of the intersection is the length of the resulting segment or 0 in case the intersection is an empty set.
For example, the intersection of segments [1;5] and [3;10] is [3;5] (length 2), the intersection of segments [1;5] and [5;7] is [5;5] (length 0) and the intersection of segments [1;5] and [6;6] is an empty set (length 0).
Your task is to remove exactly one segment from the given sequence in such a way that the intersection of the remaining (n - 1) segments has the maximal possible length.
Input
The first line contains a single integer n (2 β€ n β€ 3 β
10^5) β the number of segments in the sequence.
Each of the next n lines contains two integers l_i and r_i (0 β€ l_i β€ r_i β€ 10^9) β the description of the i-th segment.
Output
Print a single integer β the maximal possible length of the intersection of (n - 1) remaining segments after you remove exactly one segment from the sequence.
Examples
Input
4
1 3
2 6
0 4
3 3
Output
1
Input
5
2 6
1 3
0 4
1 20
0 4
Output
2
Input
3
4 5
1 2
9 20
Output
0
Input
2
3 10
1 5
Output
7
Note
In the first example you should remove the segment [3;3], the intersection will become [2;3] (length 1). Removing any other segment will result in the intersection [3;3] (length 0).
In the second example you should remove the segment [1;3] or segment [2;6], the intersection will become [2;4] (length 2) or [1;3] (length 2), respectively. Removing any other segment will result in the intersection [2;3] (length 1).
In the third example the intersection will become an empty set no matter the segment you remove.
In the fourth example you will get the intersection [3;10] (length 7) if you remove the segment [1;5] or the intersection [1;5] (length 4) if you remove the segment [3;10].
Submitted Solution:
```
from operator import itemgetter
n = int(input())
lines = sorted([list(map(int, input().split())) for i in range(n)], key=itemgetter(0))
if lines[0][1] <= lines[1][0]:
lines.pop(0)
elif lines[-1][0] >= lines[-2][1]:
lines.pop(-1)
else:
lowest_width_id = None
lowest_width = None
for index, (a, b) in enumerate(lines):
if lowest_width is None:
lowest_width = b - a
lowest_width_id = index
else:
if (b - a) < lowest_width:
lowest_width = b - a
lowest_width_id = index
first_width = (lines[0][1] - lines[1][0])
last_width = (lines[-2][1] - lines[-1][0])
pooped = False
if first_width < last_width:
if first_width < lowest_width:
lines.pop(0)
pooped = True
elif first_width > last_width:
if last_width < lowest_width:
lines.pop(-1)
pooped = True
if not pooped:
lines.pop(lowest_width_id)
left = None
right = None
for a, b in lines:
if left is None or left < a:
left = a
if right is None or right > b:
right = b
print(max(0, right - left))
``` | instruction | 0 | 39,614 | 23 | 79,228 |
No | output | 1 | 39,614 | 23 | 79,229 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n segments on a number line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.
The intersection of a sequence of segments is such a maximal set of points (not necesserily having integer coordinates) that each point lies within every segment from the sequence. If the resulting set isn't empty, then it always forms some continuous segment. The length of the intersection is the length of the resulting segment or 0 in case the intersection is an empty set.
For example, the intersection of segments [1;5] and [3;10] is [3;5] (length 2), the intersection of segments [1;5] and [5;7] is [5;5] (length 0) and the intersection of segments [1;5] and [6;6] is an empty set (length 0).
Your task is to remove exactly one segment from the given sequence in such a way that the intersection of the remaining (n - 1) segments has the maximal possible length.
Input
The first line contains a single integer n (2 β€ n β€ 3 β
10^5) β the number of segments in the sequence.
Each of the next n lines contains two integers l_i and r_i (0 β€ l_i β€ r_i β€ 10^9) β the description of the i-th segment.
Output
Print a single integer β the maximal possible length of the intersection of (n - 1) remaining segments after you remove exactly one segment from the sequence.
Examples
Input
4
1 3
2 6
0 4
3 3
Output
1
Input
5
2 6
1 3
0 4
1 20
0 4
Output
2
Input
3
4 5
1 2
9 20
Output
0
Input
2
3 10
1 5
Output
7
Note
In the first example you should remove the segment [3;3], the intersection will become [2;3] (length 1). Removing any other segment will result in the intersection [3;3] (length 0).
In the second example you should remove the segment [1;3] or segment [2;6], the intersection will become [2;4] (length 2) or [1;3] (length 2), respectively. Removing any other segment will result in the intersection [2;3] (length 1).
In the third example the intersection will become an empty set no matter the segment you remove.
In the fourth example you will get the intersection [3;10] (length 7) if you remove the segment [1;5] or the intersection [1;5] (length 4) if you remove the segment [3;10].
Submitted Solution:
```
N = int( input())
X = [ list( map( int, input().split())) for _ in range(N)]
X.sort(key = lambda x:x[1], reverse=0)
A = [X[0][0],X[0][1]]
B = [0,10**9]
for i in range(1, N):
a, b = X[i]
if max( A[1] - A[0], 0) > max( 0, min(B[1],b) - max(B[0],a)):
B[0], B[1] = A[0], A[1]
else:
B[0] = max( B[0], a)
B[1] = min( B[1], b)
A = [ max(A[0], a), min(A[1], b)]
print( max(0, B[1] - B[0],A[1]-A[0]))
``` | instruction | 0 | 39,615 | 23 | 79,230 |
No | output | 1 | 39,615 | 23 | 79,231 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n points on a plane. The i-th point has coordinates (x_i, y_i). You have two horizontal platforms, both of length k. Each platform can be placed anywhere on a plane but it should be placed horizontally (on the same y-coordinate) and have integer borders. If the left border of the platform is (x, y) then the right border is (x + k, y) and all points between borders (including borders) belong to the platform.
Note that platforms can share common points (overlap) and it is not necessary to place both platforms on the same y-coordinate.
When you place both platforms on a plane, all points start falling down decreasing their y-coordinate. If a point collides with some platform at some moment, the point stops and is saved. Points which never collide with any platform are lost.
Your task is to find the maximum number of points you can save if you place both platforms optimally.
You have to answer t independent test cases.
For better understanding, please read the Note section below to see a picture for the first test case.
Input
The first line of the input contains one integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. Then t test cases follow.
The first line of the test case contains two integers n and k (1 β€ n β€ 2 β
10^5; 1 β€ k β€ 10^9) β the number of points and the length of each platform, respectively. The second line of the test case contains n integers x_1, x_2, ..., x_n (1 β€ x_i β€ 10^9), where x_i is x-coordinate of the i-th point. The third line of the input contains n integers y_1, y_2, ..., y_n (1 β€ y_i β€ 10^9), where y_i is y-coordinate of the i-th point. All points are distinct (there is no pair 1 β€ i < j β€ n such that x_i = x_j and y_i = y_j).
It is guaranteed that the sum of n does not exceed 2 β
10^5 (β n β€ 2 β
10^5).
Output
For each test case, print the answer: the maximum number of points you can save if you place both platforms optimally.
Example
Input
4
7 1
1 5 2 3 1 5 4
1 3 6 7 2 5 4
1 1
1000000000
1000000000
5 10
10 7 5 15 8
20 199 192 219 1904
10 10
15 19 8 17 20 10 9 2 10 19
12 13 6 17 1 14 7 9 19 3
Output
6
1
5
10
Note
The picture corresponding to the first test case of the example:
<image>
Blue dots represent the points, red segments represent the platforms. One of the possible ways is to place the first platform between points (1, -1) and (2, -1) and the second one between points (4, 3) and (5, 3). Vectors represent how the points will fall down. As you can see, the only point we can't save is the point (3, 7) so it falls down infinitely and will be lost. It can be proven that we can't achieve better answer here. Also note that the point (5, 3) doesn't fall at all because it is already on the platform. | instruction | 0 | 39,786 | 23 | 79,572 |
Tags: binary search, dp, sortings, two pointers
Correct Solution:
```
import sys
from bisect import bisect_right as br
input = sys.stdin.readline
for _ in range(int(input())):
n, k = map(int, input().split())
xs = list(map(int, input().split()))
input()
xs.sort()
lmax = [0] * (n + 1)
rmax = [0] * (n + 1)
for l in range(n):
r = br(xs, xs[l] + k)
lmax[l] = r - l
rmax[r] = max(rmax[r], r - l)
#print(xs, lmax, rmax)
for i in range(n, 0, -1): lmax[i - 1] = max(lmax[i - 1], lmax[i])
for i in range(n): rmax[i + 1] = max(rmax[i + 1], rmax[i])
res = 0
for i in range(n + 1): res = max(res, lmax[i] + rmax[i])
print(res)
``` | output | 1 | 39,786 | 23 | 79,573 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n points on a plane. The i-th point has coordinates (x_i, y_i). You have two horizontal platforms, both of length k. Each platform can be placed anywhere on a plane but it should be placed horizontally (on the same y-coordinate) and have integer borders. If the left border of the platform is (x, y) then the right border is (x + k, y) and all points between borders (including borders) belong to the platform.
Note that platforms can share common points (overlap) and it is not necessary to place both platforms on the same y-coordinate.
When you place both platforms on a plane, all points start falling down decreasing their y-coordinate. If a point collides with some platform at some moment, the point stops and is saved. Points which never collide with any platform are lost.
Your task is to find the maximum number of points you can save if you place both platforms optimally.
You have to answer t independent test cases.
For better understanding, please read the Note section below to see a picture for the first test case.
Input
The first line of the input contains one integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. Then t test cases follow.
The first line of the test case contains two integers n and k (1 β€ n β€ 2 β
10^5; 1 β€ k β€ 10^9) β the number of points and the length of each platform, respectively. The second line of the test case contains n integers x_1, x_2, ..., x_n (1 β€ x_i β€ 10^9), where x_i is x-coordinate of the i-th point. The third line of the input contains n integers y_1, y_2, ..., y_n (1 β€ y_i β€ 10^9), where y_i is y-coordinate of the i-th point. All points are distinct (there is no pair 1 β€ i < j β€ n such that x_i = x_j and y_i = y_j).
It is guaranteed that the sum of n does not exceed 2 β
10^5 (β n β€ 2 β
10^5).
Output
For each test case, print the answer: the maximum number of points you can save if you place both platforms optimally.
Example
Input
4
7 1
1 5 2 3 1 5 4
1 3 6 7 2 5 4
1 1
1000000000
1000000000
5 10
10 7 5 15 8
20 199 192 219 1904
10 10
15 19 8 17 20 10 9 2 10 19
12 13 6 17 1 14 7 9 19 3
Output
6
1
5
10
Note
The picture corresponding to the first test case of the example:
<image>
Blue dots represent the points, red segments represent the platforms. One of the possible ways is to place the first platform between points (1, -1) and (2, -1) and the second one between points (4, 3) and (5, 3). Vectors represent how the points will fall down. As you can see, the only point we can't save is the point (3, 7) so it falls down infinitely and will be lost. It can be proven that we can't achieve better answer here. Also note that the point (5, 3) doesn't fall at all because it is already on the platform. | instruction | 0 | 39,787 | 23 | 79,574 |
Tags: binary search, dp, sortings, two pointers
Correct Solution:
```
import io
import os
from collections import Counter, defaultdict, deque
def solve(N, K, X, Y):
X = sorted(X)
def maxSave(A, rev=False):
window = deque()
dp = []
mx = 0
dp.append(mx)
for x in A:
window.append(x)
while abs(window[-1] - window[0]) > K:
window.popleft()
mx = max(mx, len(window))
dp.append(mx)
return dp
forward = maxSave(X)
backward = maxSave(X[::-1], True)
best = 0
for i in range(N + 1):
best = max(best, forward[i] + backward[N - i])
return best
if __name__ == "__main__":
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
TC = int(input())
for tc in range(1, TC + 1):
N, K = [int(x) for x in input().split()]
X = [int(x) for x in input().split()]
Y = [int(x) for x in input().split()]
ans = solve(N, K, X, Y)
print(ans)
``` | output | 1 | 39,787 | 23 | 79,575 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n points on a plane. The i-th point has coordinates (x_i, y_i). You have two horizontal platforms, both of length k. Each platform can be placed anywhere on a plane but it should be placed horizontally (on the same y-coordinate) and have integer borders. If the left border of the platform is (x, y) then the right border is (x + k, y) and all points between borders (including borders) belong to the platform.
Note that platforms can share common points (overlap) and it is not necessary to place both platforms on the same y-coordinate.
When you place both platforms on a plane, all points start falling down decreasing their y-coordinate. If a point collides with some platform at some moment, the point stops and is saved. Points which never collide with any platform are lost.
Your task is to find the maximum number of points you can save if you place both platforms optimally.
You have to answer t independent test cases.
For better understanding, please read the Note section below to see a picture for the first test case.
Input
The first line of the input contains one integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. Then t test cases follow.
The first line of the test case contains two integers n and k (1 β€ n β€ 2 β
10^5; 1 β€ k β€ 10^9) β the number of points and the length of each platform, respectively. The second line of the test case contains n integers x_1, x_2, ..., x_n (1 β€ x_i β€ 10^9), where x_i is x-coordinate of the i-th point. The third line of the input contains n integers y_1, y_2, ..., y_n (1 β€ y_i β€ 10^9), where y_i is y-coordinate of the i-th point. All points are distinct (there is no pair 1 β€ i < j β€ n such that x_i = x_j and y_i = y_j).
It is guaranteed that the sum of n does not exceed 2 β
10^5 (β n β€ 2 β
10^5).
Output
For each test case, print the answer: the maximum number of points you can save if you place both platforms optimally.
Example
Input
4
7 1
1 5 2 3 1 5 4
1 3 6 7 2 5 4
1 1
1000000000
1000000000
5 10
10 7 5 15 8
20 199 192 219 1904
10 10
15 19 8 17 20 10 9 2 10 19
12 13 6 17 1 14 7 9 19 3
Output
6
1
5
10
Note
The picture corresponding to the first test case of the example:
<image>
Blue dots represent the points, red segments represent the platforms. One of the possible ways is to place the first platform between points (1, -1) and (2, -1) and the second one between points (4, 3) and (5, 3). Vectors represent how the points will fall down. As you can see, the only point we can't save is the point (3, 7) so it falls down infinitely and will be lost. It can be proven that we can't achieve better answer here. Also note that the point (5, 3) doesn't fall at all because it is already on the platform. | instruction | 0 | 39,788 | 23 | 79,576 |
Tags: binary search, dp, sortings, two pointers
Correct Solution:
```
import sys
input = sys.stdin.buffer.readline
def print(val):
sys.stdout.write(str(val) + '\n')
def prog():
for _ in range(int(input())):
n,k = map(int,input().split())
x = list(map(int,input().split()))
y = list(map(int,input().split()))
x.sort()
most_at_point = [0]*n
most_after_point = [0]*(n+1)
tot = 0
j = -1
for i in range(n):
while j + 1 < n and x[j + 1] <= x[i] + k:
j += 1
tot += 1
most_at_point[i] = tot
tot -= 1
for i in range(n-1,-1,-1):
most_after_point[i] = max(most_after_point[i+1], most_at_point[i])
best = 0
j = 0
for i in range(n):
while j < n and x[j] <= x[i] + k:
j += 1
if j == n:
best = max(best, most_at_point[i])
else:
best = max(best, most_at_point[i] + most_after_point[j])
print(best)
prog()
``` | output | 1 | 39,788 | 23 | 79,577 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n points on a plane. The i-th point has coordinates (x_i, y_i). You have two horizontal platforms, both of length k. Each platform can be placed anywhere on a plane but it should be placed horizontally (on the same y-coordinate) and have integer borders. If the left border of the platform is (x, y) then the right border is (x + k, y) and all points between borders (including borders) belong to the platform.
Note that platforms can share common points (overlap) and it is not necessary to place both platforms on the same y-coordinate.
When you place both platforms on a plane, all points start falling down decreasing their y-coordinate. If a point collides with some platform at some moment, the point stops and is saved. Points which never collide with any platform are lost.
Your task is to find the maximum number of points you can save if you place both platforms optimally.
You have to answer t independent test cases.
For better understanding, please read the Note section below to see a picture for the first test case.
Input
The first line of the input contains one integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. Then t test cases follow.
The first line of the test case contains two integers n and k (1 β€ n β€ 2 β
10^5; 1 β€ k β€ 10^9) β the number of points and the length of each platform, respectively. The second line of the test case contains n integers x_1, x_2, ..., x_n (1 β€ x_i β€ 10^9), where x_i is x-coordinate of the i-th point. The third line of the input contains n integers y_1, y_2, ..., y_n (1 β€ y_i β€ 10^9), where y_i is y-coordinate of the i-th point. All points are distinct (there is no pair 1 β€ i < j β€ n such that x_i = x_j and y_i = y_j).
It is guaranteed that the sum of n does not exceed 2 β
10^5 (β n β€ 2 β
10^5).
Output
For each test case, print the answer: the maximum number of points you can save if you place both platforms optimally.
Example
Input
4
7 1
1 5 2 3 1 5 4
1 3 6 7 2 5 4
1 1
1000000000
1000000000
5 10
10 7 5 15 8
20 199 192 219 1904
10 10
15 19 8 17 20 10 9 2 10 19
12 13 6 17 1 14 7 9 19 3
Output
6
1
5
10
Note
The picture corresponding to the first test case of the example:
<image>
Blue dots represent the points, red segments represent the platforms. One of the possible ways is to place the first platform between points (1, -1) and (2, -1) and the second one between points (4, 3) and (5, 3). Vectors represent how the points will fall down. As you can see, the only point we can't save is the point (3, 7) so it falls down infinitely and will be lost. It can be proven that we can't achieve better answer here. Also note that the point (5, 3) doesn't fall at all because it is already on the platform. | instruction | 0 | 39,789 | 23 | 79,578 |
Tags: binary search, dp, sortings, two pointers
Correct Solution:
```
for _ in range(int(input())):
n,k=map(int,input().split())
x,y=[int(i) for i in input().split()],[int(i) for i in input().split()]
x.sort()
x.append(9999999999999999999)
t,ans,arr,r=0,0,[0]*(n+5),0
ll=0
for i in range(n):
while(x[r+1]-x[i]<=k):r=r+1
can=r-i+1
arr[i]=(can,x[i]+k+1)
while(ll<=i and (arr[ll])[1]<x[i]):
t=max([t,(arr[ll])[0]])
ll=ll+1
ans=max([ans,can+t])
r=0
for i in range(n):
while(x[r+1]-x[i]<=k*2+1):r=r+1
ans=max([ans,r-i+1])
print(ans)
``` | output | 1 | 39,789 | 23 | 79,579 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n points on a plane. The i-th point has coordinates (x_i, y_i). You have two horizontal platforms, both of length k. Each platform can be placed anywhere on a plane but it should be placed horizontally (on the same y-coordinate) and have integer borders. If the left border of the platform is (x, y) then the right border is (x + k, y) and all points between borders (including borders) belong to the platform.
Note that platforms can share common points (overlap) and it is not necessary to place both platforms on the same y-coordinate.
When you place both platforms on a plane, all points start falling down decreasing their y-coordinate. If a point collides with some platform at some moment, the point stops and is saved. Points which never collide with any platform are lost.
Your task is to find the maximum number of points you can save if you place both platforms optimally.
You have to answer t independent test cases.
For better understanding, please read the Note section below to see a picture for the first test case.
Input
The first line of the input contains one integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. Then t test cases follow.
The first line of the test case contains two integers n and k (1 β€ n β€ 2 β
10^5; 1 β€ k β€ 10^9) β the number of points and the length of each platform, respectively. The second line of the test case contains n integers x_1, x_2, ..., x_n (1 β€ x_i β€ 10^9), where x_i is x-coordinate of the i-th point. The third line of the input contains n integers y_1, y_2, ..., y_n (1 β€ y_i β€ 10^9), where y_i is y-coordinate of the i-th point. All points are distinct (there is no pair 1 β€ i < j β€ n such that x_i = x_j and y_i = y_j).
It is guaranteed that the sum of n does not exceed 2 β
10^5 (β n β€ 2 β
10^5).
Output
For each test case, print the answer: the maximum number of points you can save if you place both platforms optimally.
Example
Input
4
7 1
1 5 2 3 1 5 4
1 3 6 7 2 5 4
1 1
1000000000
1000000000
5 10
10 7 5 15 8
20 199 192 219 1904
10 10
15 19 8 17 20 10 9 2 10 19
12 13 6 17 1 14 7 9 19 3
Output
6
1
5
10
Note
The picture corresponding to the first test case of the example:
<image>
Blue dots represent the points, red segments represent the platforms. One of the possible ways is to place the first platform between points (1, -1) and (2, -1) and the second one between points (4, 3) and (5, 3). Vectors represent how the points will fall down. As you can see, the only point we can't save is the point (3, 7) so it falls down infinitely and will be lost. It can be proven that we can't achieve better answer here. Also note that the point (5, 3) doesn't fall at all because it is already on the platform. | instruction | 0 | 39,790 | 23 | 79,580 |
Tags: binary search, dp, sortings, two pointers
Correct Solution:
```
def ans(n, k, x, y):
x.sort()
l = [0]*len(x)
r = [0]*len(x)
i = 0
j = 0
temp = 0
while(i<len(x) and j<len(x)):
temp = i-j+1
if i==j:
l[i] = temp
i+=1
else:
if x[i]-x[j]<=k:
l[i] = temp
i+=1
else:
j+=1
i = n-1
j = n-1
temp = 0
while(i>=0 and j>=0):
temp = j-i+1
if i==j:
r[i] = temp
i -= 1
else:
if x[j]-x[i]<=k:
r[i] = temp
i -= 1
else:
j -= 1
#correct till here
prefix = [0]*len(x)
suffix = [0]*len(x)
prefix[0] = l[0]
suffix[-1] = r[-1]
for i in range(1, len(x)):
prefix[i] = max(l[i],prefix[i-1])
for i in range(len(x)-2,-1,-1):
suffix[i] = max(r[i],suffix[i+1])
answer = 1
for i in range(n-1):
answer = max(answer, prefix[i]+suffix[i+1])
print(answer)
m = int(input())
for i in range(m):
arr = input().split()
n = int(arr[0])
k = int(arr[1])
a = input().split()
b = input().split()
x = []
y = []
for j in a:
x.append(int(j))
for j in b:
y.append(int(j))
ans(n, k, x, y)
``` | output | 1 | 39,790 | 23 | 79,581 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n points on a plane. The i-th point has coordinates (x_i, y_i). You have two horizontal platforms, both of length k. Each platform can be placed anywhere on a plane but it should be placed horizontally (on the same y-coordinate) and have integer borders. If the left border of the platform is (x, y) then the right border is (x + k, y) and all points between borders (including borders) belong to the platform.
Note that platforms can share common points (overlap) and it is not necessary to place both platforms on the same y-coordinate.
When you place both platforms on a plane, all points start falling down decreasing their y-coordinate. If a point collides with some platform at some moment, the point stops and is saved. Points which never collide with any platform are lost.
Your task is to find the maximum number of points you can save if you place both platforms optimally.
You have to answer t independent test cases.
For better understanding, please read the Note section below to see a picture for the first test case.
Input
The first line of the input contains one integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. Then t test cases follow.
The first line of the test case contains two integers n and k (1 β€ n β€ 2 β
10^5; 1 β€ k β€ 10^9) β the number of points and the length of each platform, respectively. The second line of the test case contains n integers x_1, x_2, ..., x_n (1 β€ x_i β€ 10^9), where x_i is x-coordinate of the i-th point. The third line of the input contains n integers y_1, y_2, ..., y_n (1 β€ y_i β€ 10^9), where y_i is y-coordinate of the i-th point. All points are distinct (there is no pair 1 β€ i < j β€ n such that x_i = x_j and y_i = y_j).
It is guaranteed that the sum of n does not exceed 2 β
10^5 (β n β€ 2 β
10^5).
Output
For each test case, print the answer: the maximum number of points you can save if you place both platforms optimally.
Example
Input
4
7 1
1 5 2 3 1 5 4
1 3 6 7 2 5 4
1 1
1000000000
1000000000
5 10
10 7 5 15 8
20 199 192 219 1904
10 10
15 19 8 17 20 10 9 2 10 19
12 13 6 17 1 14 7 9 19 3
Output
6
1
5
10
Note
The picture corresponding to the first test case of the example:
<image>
Blue dots represent the points, red segments represent the platforms. One of the possible ways is to place the first platform between points (1, -1) and (2, -1) and the second one between points (4, 3) and (5, 3). Vectors represent how the points will fall down. As you can see, the only point we can't save is the point (3, 7) so it falls down infinitely and will be lost. It can be proven that we can't achieve better answer here. Also note that the point (5, 3) doesn't fall at all because it is already on the platform. | instruction | 0 | 39,791 | 23 | 79,582 |
Tags: binary search, dp, sortings, two pointers
Correct Solution:
```
T = int(input())
for case in range(T):
n,k=map(int,input().split())
x=list(map(int,input().split()))
y=list(map(int,input().split()))
suf=[0 for i in range(n+2)]
ans=[0 for i in range(n+2)]
x=sorted(x)
j=0
for i in range(n):
while j<n and x[j]<=x[i]+k:
j+=1
ans[i]=j-i
for i in range(n-1,-1,-1):
suf[i]=max(ans[i],suf[i+1])
mx=0
for i in range(n):
mx=max(mx,ans[i]+suf[min(n,ans[i]+i)])
print(mx)
``` | output | 1 | 39,791 | 23 | 79,583 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There are n points on a plane. The i-th point has coordinates (x_i, y_i). You have two horizontal platforms, both of length k. Each platform can be placed anywhere on a plane but it should be placed horizontally (on the same y-coordinate) and have integer borders. If the left border of the platform is (x, y) then the right border is (x + k, y) and all points between borders (including borders) belong to the platform.
Note that platforms can share common points (overlap) and it is not necessary to place both platforms on the same y-coordinate.
When you place both platforms on a plane, all points start falling down decreasing their y-coordinate. If a point collides with some platform at some moment, the point stops and is saved. Points which never collide with any platform are lost.
Your task is to find the maximum number of points you can save if you place both platforms optimally.
You have to answer t independent test cases.
For better understanding, please read the Note section below to see a picture for the first test case.
Input
The first line of the input contains one integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. Then t test cases follow.
The first line of the test case contains two integers n and k (1 β€ n β€ 2 β
10^5; 1 β€ k β€ 10^9) β the number of points and the length of each platform, respectively. The second line of the test case contains n integers x_1, x_2, ..., x_n (1 β€ x_i β€ 10^9), where x_i is x-coordinate of the i-th point. The third line of the input contains n integers y_1, y_2, ..., y_n (1 β€ y_i β€ 10^9), where y_i is y-coordinate of the i-th point. All points are distinct (there is no pair 1 β€ i < j β€ n such that x_i = x_j and y_i = y_j).
It is guaranteed that the sum of n does not exceed 2 β
10^5 (β n β€ 2 β
10^5).
Output
For each test case, print the answer: the maximum number of points you can save if you place both platforms optimally.
Example
Input
4
7 1
1 5 2 3 1 5 4
1 3 6 7 2 5 4
1 1
1000000000
1000000000
5 10
10 7 5 15 8
20 199 192 219 1904
10 10
15 19 8 17 20 10 9 2 10 19
12 13 6 17 1 14 7 9 19 3
Output
6
1
5
10
Note
The picture corresponding to the first test case of the example:
<image>
Blue dots represent the points, red segments represent the platforms. One of the possible ways is to place the first platform between points (1, -1) and (2, -1) and the second one between points (4, 3) and (5, 3). Vectors represent how the points will fall down. As you can see, the only point we can't save is the point (3, 7) so it falls down infinitely and will be lost. It can be proven that we can't achieve better answer here. Also note that the point (5, 3) doesn't fall at all because it is already on the platform. | instruction | 0 | 39,792 | 23 | 79,584 |
Tags: binary search, dp, sortings, two pointers
Correct Solution:
```
t=int(input());f=input
for _ in range(t):
n,k=map(int,f().split());x=sorted(map(int,f().split()));f();r=[0]*n;c=n-1
for i in range(n-1,-1,-1):
while x[c] > x[i] + k:
c-=1
r[i]=c
m=[0]*n;c=0
for i in range(n-1,-1,-1):
m[i]=c
c=max(r[i]-i+1,c)
o=[r[i]-i+1+m[r[i]] for i in range(n)]
print(max(o))
``` | output | 1 | 39,792 | 23 | 79,585 |
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