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 |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####. | instruction | 0 | 11,472 | 23 | 22,944 |
"Correct Solution:
```
a, b = map(int, input().split())
print(41, 100)
for _ in range(10):
for _ in range(50):
print('.', end='')
if b>1:
print('#', end='')
b -= 1
else:
print('.', end='')
print()
print('.'*100)
print('#'*100)
for _ in range(10):
for _ in range(50):
print('#', end='')
if a>1:
print('.', end='')
a -= 1
else:
print('#', end='')
print()
print('#'*100)
``` | output | 1 | 11,472 | 23 | 22,945 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####. | instruction | 0 | 11,473 | 23 | 22,946 |
"Correct Solution:
```
a, b = map(int, input().split())
a -= 1
b -= 1
ans = [["#" for _ in range(90)] for _ in range(40)] + [["." for _ in range(90)] for _ in range(40)]
pos = 0
for i in range(a):
x = pos % 90
y = (pos // 90) * 2
ans[y][x] = "."
pos += 2
pos = 0
for j in range(b):
x = pos % 90
y = 45 + (pos // 90) * 2
ans[y][x] = "#"
pos += 2
print(80, 90)
for row in ans:
print("".join(row))
``` | output | 1 | 11,473 | 23 | 22,947 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####. | instruction | 0 | 11,474 | 23 | 22,948 |
"Correct Solution:
```
# editorial参照
# 格子まで詰め込もうとしたのが困難
# 十分大きい黒白の塊一つに孤立した白黒の点を取る
a,b = map(int, input().split( ))
k=50
W = [["."]*(k*2) for i in range(k)]
B = [["#"]*(k*2) for i in range(k)]
for i in range(b-1):
h = (i//k)*2
w = (i%k)*2
W[h][w]="#"
for i in range(a-1):
h = (i//k)*2+1
w = (i%k)*2+1
B[-h][-w]="."
ans = [''.join(W[i]) for i in range(k)]+ [''.join(B[i]) for i in range(k)]
print(100,100)
print('\n'.join(ans))
``` | output | 1 | 11,474 | 23 | 22,949 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####. | instruction | 0 | 11,475 | 23 | 22,950 |
"Correct Solution:
```
A,B = list(map(int,input().split()))
QA=(A-1)//50
QB=(B-1)//50
RA=(A-1)%50
RB=(B-1)%50
def PRINTw(x): #x個の白１黒３ブロック
for j in range(x):
print(".#",end="")
for j in range(50-x):
print("##",end="")
print()
for j in range(100):
print("#",end="")
print()
def PRINTb(x): #x個の白３黒１ブロック
for j in range(100):
print(".",end="")
print()
for j in range(x):
print(".#",end="")
for j in range(50-x):
print("..",end="")
print()
print("40 100")
for i in range(QA):
PRINTw(50)
PRINTw(RA)
for i in range(10-(QA+1)):
PRINTw(0)
for i in range(QB):
PRINTb(50)
PRINTb(RB)
for i in range(10-(QB+1)):
PRINTb(0)
``` | output | 1 | 11,475 | 23 | 22,951 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####. | instruction | 0 | 11,476 | 23 | 22,952 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
def inpl(): return list(map(int, input().split()))
"""
1 <= A, B <= 1659まで対応してるよ
"""
A, B = inpl()
L = [["."]*50 for i in range(100)]
R = [["#"]*50 for i in range(100)]
def plot(R):
print("\n".join(["".join(r) for r in R]))
count = 0
for i in range(98):
for j in range(16):
if count == B-1:
break
L[i+1][j*3 + i%3 + 1] = "#"
count += 1
count = 0
for i in range(98):
for j in range(16):
if count == A-1:
break
R[i+1][j*3 + i%3 + 1] = "."
count += 1
ANS = [l+r for l, r in zip(L, R)]
print(100, 100)
plot(ANS)
``` | output | 1 | 11,476 | 23 | 22,953 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####. | instruction | 0 | 11,477 | 23 | 22,954 |
"Correct Solution:
```
def main():
buf = input()
buflist = buf.split()
A = int(buflist[0])
B = int(buflist[1])
board = []
for i in range(100):
board.append([])
for j in range(100):
if i < 50:
board[-1].append('#')
else:
board[-1].append('.')
A_remaining = A - 1
for i in range(0, 50, 2):
if A_remaining <= 0:
break;
for j in range(0, 100, 2):
board[i][j] = '.'
A_remaining -= 1
if A_remaining <= 0:
break;
B_remaining = B - 1
for i in range(100-1, 50-1, -2):
if B_remaining <= 0:
break;
for j in range(0, 100, 2):
board[i][j] = '#'
B_remaining -= 1
if B_remaining <= 0:
break;
print(100, 100)
for i in range(100):
print(''.join(board[i]))
if __name__ == '__main__':
main()
``` | output | 1 | 11,477 | 23 | 22,955 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####. | instruction | 0 | 11,478 | 23 | 22,956 |
"Correct Solution:
```
from math import gcd
from math import factorial as f
from math import ceil, floor, sqrt
import math
import bisect
import re
import heapq
from copy import deepcopy
import itertools
from itertools import permutations
from sys import exit
ii = lambda: int(input())
mi = lambda: map(int, input().split())
li = lambda: list(map(int, input().split()))
yes = "Yes"
no = "No"
def main():
a, b = mi()
print(100, 100)
ans = [[] for i in range(100)]
for i in range(50):
for j in range(100):
ans[i].append('#')
for i in range(50, 100):
for j in range(100):
ans[i].append('.')
for i in range(a - 1):
ans[2 * (i // 50)][2 * (i % 50)] = '.'
for i in range(b - 1):
ans[99 - 2 * (i // 50)][2 * (i % 50)] = '#'
for i in range(100):
print(''.join(ans[i]))
main()
``` | output | 1 | 11,478 | 23 | 22,957 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####. | instruction | 0 | 11,479 | 23 | 22,958 |
"Correct Solution:
```
import sys
import math
import collections
import bisect
import itertools
# import numpy as np
sys.setrecursionlimit(10 ** 7)
INF = 10 ** 16
MOD = 10 ** 9 + 7
# MOD = 998244353
ni = lambda: int(sys.stdin.readline().rstrip())
ns = lambda: map(int, sys.stdin.readline().rstrip().split())
na = lambda: list(map(int, sys.stdin.readline().rstrip().split()))
na1 = lambda: list(map(lambda x: int(x) - 1, sys.stdin.readline().rstrip().split()))
# ===CODE===
def main():
w, b = ns()
l = 100
mat = [["#" for _ in range(l)] for __ in range(l)]
if w == 1 and b == 1:
mat[0][0] = "."
cnt = 0
breakflg = False
tmp = 1 if b > 1 else 0
flg = False
for i in range(0, l - 3, 3):
for j in range(0, l - 3, 3):
if not flg:
if cnt < w - tmp:
around = "#"
center = "."
else:
flg = True
break
if flg:
if cnt < w - tmp + b - 1:
around = "."
center = "#"
else:
breakflg = True
break
for n in range(3):
for m in range(3):
mat[i + n][j + m] = center if n == 1 and m == 1 else around
cnt += 1
if breakflg:
break
print(l, l)
for mi in mat:
print(*mi, sep="")
if __name__ == '__main__':
main()
``` | output | 1 | 11,479 | 23 | 22,959 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####.
Submitted Solution:
```
# D
A, B = map(int, input().split())
res_list = [["."]*100 for _ in range(20)] + [["#"]*100 for _ in range(20)]
A -= 1
B -= 1
for i in range(0, 20, 2):
for j in range(0, 100, 2):
if B > 0:
res_list[i][j] = "#"
B -= 1
for i in range(21, 40, 2):
for j in range(0, 100, 2):
if A > 0:
res_list[i][j] = "."
A -= 1
print("40 100")
for res in res_list:
print("".join(res))
``` | instruction | 0 | 11,480 | 23 | 22,960 |
Yes | output | 1 | 11,480 | 23 | 22,961 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####.
Submitted Solution:
```
a,b = map(int,input().split())
ans = [["." for i in range(100)] for j in range(100)]
for i in range(100):
for j in range(50):
ans[i][j] = "#"
a-=1
b-=1
ind = 0
while True:
loop = min(a,25)
for i in range(loop):
ans[ind][i*2] = "."
a-=loop
ind += 2
if a == 0:
break
ind = 0
while True:
loop = min(b,25)
for i in range(loop):
ans[ind][51+i*2] = "#"
b-=loop
ind += 2
if b == 0:
break
print("100 100")
for i in range(100):
for j in range(99):
print(ans[i][j],end="")
print(ans[i][-1])
``` | instruction | 0 | 11,481 | 23 | 22,962 |
Yes | output | 1 | 11,481 | 23 | 22,963 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####.
Submitted Solution:
```
a,b = map(int,input().split())
print("40 100")
kuro = [["#" for i in range(100)] for j in range(20)]
siro = [["." for i in range(100)] for j in range(20)]
cou = 0
flag = False
for i in range(0,20,2):
if flag:
break
for j in range(0,100,2):
if cou >= a-1:
flag = True
break
elif cou < a-1:
cou += 1
kuro[i][j] = "."
cou = 0
flag = False
for i in range(1,20,2):
if flag:
break
for j in range(0,100,2):
if cou >= b-1:
flag = True
break
elif cou < b-1:
cou += 1
siro[i][j] = "#"
for i in range(20):
for j in range(100):
print(kuro[i][j],end="")
print()
for i in range(20):
for j in range(100):
print(siro[i][j],end="")
print()
``` | instruction | 0 | 11,482 | 23 | 22,964 |
Yes | output | 1 | 11,482 | 23 | 22,965 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####.
Submitted Solution:
```
A, B = map(int, input().split())
N = 100
board = [['.#'[row >= N//2] for _ in range(N)] for row in range(N)]
for i in range(B-1):
r, c = i // 25 * 2, (i % 25) * 2
board[r][c] = "#"
for i in range(A-1):
r, c = i // 25 * 2, (i % 25) * 2
board[-r-1][c] = "."
print(N, N)
print("\n".join(''.join(row) for row in board))
``` | instruction | 0 | 11,483 | 23 | 22,966 |
Yes | output | 1 | 11,483 | 23 | 22,967 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####.
Submitted Solution:
```
a,b=map(int,input().split())
grid=[["." for i in range(100)] for j in range(50)]+[["#" for i in range(100)] for j in range(50)]
white=0;black=0
for i in range(49):
for j in range(100):
if i%2==j%2:
grid[i][j]="#"
black+=1
if black==b-1:break
if black==b-1:break
for i in range(51,100):
for j in range(100):
if i%2==j%2:
grid[i][j]="."
white+=1
if white==a-1:break
if white==a-1:break
for i in range(100):
stri=""
for j in grid[i]:
stri+=j
print(stri)
``` | instruction | 0 | 11,484 | 23 | 22,968 |
No | output | 1 | 11,484 | 23 | 22,969 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####.
Submitted Solution:
```
a, b = map(int, input().split())
N = 100
f = [['#'] * N if i < (N/2) else ['.'] * N for i in range(N)]
for i in range(a-1):
h = 2 * ((2 * i) // N)
w = (2 * i) % N
print(h, w)
f[h][w] = '.'
for i in range(b-1):
h = (N//2 + 1) + 2 * (2 * i // N)
w = 2 * i % N
print(h, w)
f[h][w] = '#'
print(N, N)
for line in f:
print(''.join(line))
``` | instruction | 0 | 11,485 | 23 | 22,970 |
No | output | 1 | 11,485 | 23 | 22,971 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####.
Submitted Solution:
```
import sys
sys.setrecursionlimit(10 ** 8)
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
A, B = map(int, readline().split())
color_flipped = False
if A < B:
A, B = B, A
color_flipped = True
def solve():
hb = min(A, 12)
h = hb * 2 * 3
w = 100
# If not flipped, False -> White (A), True -> Black (B)
grid = [[None] * w for _ in range(h)]
for i in range(hb):
for c in range(w):
for j in range(3):
grid[6 * i + j][c] = False
grid[6 * i + 3 + j][c] = i < B
black = min(hb, B)
white = black + 1
def paint_black(i):
nonlocal black
for c in range(0, w, 2):
if black == B:
return
grid[6 * i + 1][c] = True
black += 1
def paint_white(i):
nonlocal white
for c in range(0, w, 2):
if white == A:
return
grid[6 * i + 4][c] = False
white += 1
for i in range(hb):
paint_black(i)
paint_white(i)
return grid
def print_grid(grid):
h, w = len(grid), len(grid[0])
print(h, w)
for r in range(h):
for c in range(w):
if grid[r][c] ^ color_flipped:
print("#", end="")
else:
print(".", end="")
print()
if __name__ == "__main__":
print_grid(solve())
``` | instruction | 0 | 11,486 | 23 | 22,972 |
No | output | 1 | 11,486 | 23 | 22,973 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers A and B.
Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:
* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.
It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.
Constraints
* 1 \leq A \leq 500
* 1 \leq B \leq 500
Input
Input is given from Standard Input in the following format:
A B
Output
Output should be in the following format:
* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.
Examples
Input
2 3
Output
3 3
##.
..#
#.#
Input
7 8
Output
3 5
.#.#
.#.#.
.#.#
Input
1 1
Output
4 2
..
.
Input
3 14
Output
8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####.
Submitted Solution:
```
ansl1 = list("#" * (99 * 25))
ansl2 = list("." * (99 * 25))
a,b = map(int,input().split())
for i in range(a-1):
ansl1[2*i] = "."
for i in range(b-1):
ansl2[2*i] = "#"
print(100, 99)
for i in range(25):
print("".join(ansl1[(i*50):(i*50)+99]))
print("#"*99)
for j in range(24, -1, -1):
print("".join(ansl2[(j*50):(j*50)+99]))
print("." * 99)
``` | instruction | 0 | 11,487 | 23 | 22,974 |
No | output | 1 | 11,487 | 23 | 22,975 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland. | instruction | 0 | 11,666 | 23 | 23,332 |
Tags: binary search, sortings, two pointers
Correct Solution:
```
num = int(input())
data = [abs(int(i)) for i in input().split()]
data.sort()
def bins(a, b, n):
if a == b:
if data[a] <= n:
return a+1
else:
return a
else:
m = (a+b)//2
if data[m] <= n:
return bins(m+1,b,n)
else:
return bins(a, m, n)
sum = 0
for i in range(num):
sum += bins(i, num-1, 2*data[i]) - i - 1
#print(2*data[i] ,bins(i, num-1, 2*data[i]), bins(i, num-1, 2*data[i]) - i - 1)
print(sum)
#data = [1,2,3, 4,5,6,7,23]
#print(bins(1,6,3))
``` | output | 1 | 11,666 | 23 | 23,333 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland. | instruction | 0 | 11,667 | 23 | 23,334 |
Tags: binary search, sortings, two pointers
Correct Solution:
```
"""for p in range(int(input())):
n,k=map(int,input().split(" "))
number=input().split(" ")
chances=[k for i in range(n)]
prev=-1
prev_updated=-1
last_used=False
toSub=0
start=0
prevSub=0
if(number[0]=='1'):
prev=0
prev_updated=0
start=1
for i in range(start,n):
if(number[i]=='1'):
# print("\ni",i,"\ntoSub",toSub,"\nprevUpadted",prev_updated,"\nprev",prev,"\nlast_used",last_used)
f1=False
# toSub+=1
toSub=0
zeros=i - prev_updated - 1
if(last_used):
zeros-=1
#chances[i]-=toSub
#print(prevSub,(i - prev - 1 ) +1)
if(i - prev - 1 <= prevSub):
chances[i]-= prevSub - (i - prev - 1 ) +1
if(chances[i]<zeros):
chances[i]=zeros
toSub+= prevSub - (i - prev - 1 ) +1
f1=True
if(zeros==0 or chances[i]==0):
prev_updated=i
prev=i
last_used=False
prevSub=toSub
continue
# print("\nchances: ",chances[i],"\t\tzeroes : ",zeros,"\t\tprevSub :",prevSub)
if(chances[i]>zeros):
# print("\t\t\t\t1")
number[i-zeros]='1'
number[i]='0'
prev_updated=i-zeros
last_used=False
elif(chances[i]==zeros):
# print("\t\t\t\t2")
number[i]='0'
number[i-chances[i]]='1'
prev_updated=i-chances[i]
last_used=True
else:
# print("\t\t\t\t3")
number[i]='0'
number[i-chances[i]]='1'
prev_updated=i-chances[i]
last_used=True
prev=i
prevSub=toSub
if(prev_updated>2 and f1):
if(number[prev_updated]=='1' and number[prev_updated-1]=='0' and number[prev_updated-2]=='1'):
last_used=False
#if()
# print("\ni",i,"\ntoSub",toSub,"\nprevUpadted",prev_updated,"\nprev",prev,"\nlast_used",last_used)
# print(number)
else:
toSub=0
print(*number)
# print(chances)"""
"""class offer:
def __init__(self, n, fre):
self.num = n
self.free = fre
self.delta= n-fre
n,m,k=map(int,input().split(" "))
shovel=list(map(int,input().split(" ")))
#dicti={}
offers=[]
temp_arr=[False for i in range(n)]
for i in range(m):
p,q=map(int,input().split(" "))
if(p>k):
continue
offers.append(offer(p,q))
# dicti[p]=q
#for i in dicti:
# dicti[i].sort()
shovel.sort()
shovel=shovel[:k+1]
offers.sort(key=lambda x: x.delta/x.num,reverse=True)
bestoffer=[]
for i in offers:
if(not temp_arr[i.num]):
temp_arr[i.num]=True
bestoffer.append(i)
cost=0
for i in bestoffer:
for p in range(int(input())):
arr=list(input())
n=len(arr)
for i in range(n):
arr[i]=ord(arr[i])-96
arr.sort()
arr1=arr[:n//2]
arr2=arr[n//2:]
arr=[]
#print(arr,arr1,arr2)
i1=n//2-1
i2=n-i1-2
while (i1!=-1 and i2!=-1):
arr.append(arr1[i1])
arr.append(arr2[i2])
i1-=1
i2-=1
if(i1!=-1):
arr.append(arr1[i1])
elif(i2!=-1):
arr.append(arr2[i2])
#print(arr)
s=""
for i in range(n-1):
if(abs(arr[i]-arr[i+1])==1):
s=-1
print("No answer")
break
else:
s+=chr(arr[i]+96)
if(s!=-1):
s+=chr(arr[-1]+96)
print(s)"""
"""
n,m=map(int,input().split(" "))
seti=[]
ans=[1 for i in range(n)]
for i in range(m):
arr=list(map(int,input().split(" ")))
if(arr[0]>1):
seti.append(set(arr[1:]))
else:
m-=1
parent=[-1 for i in range(m)]
#print(seti)
for i in range(m-1):
for j in range(i+1,m):
if(parent[j]==-1):
if(len(seti[i].intersection(seti[j]))>0):
seti[i]=seti[i].union(seti[j])
parent[j]=i
#print(parent)
for i in range(m):
if(parent[i]==-1):
temp=list(seti[i])
store=len(temp)
for j in temp:
ans[j-1]=store
print(*ans)
for p in range(int(input())):
arr=list(input())
n=len(arr)
for i in range(n):
arr[i]=ord(arr[i])-96
arr.sort()
arr1=arr[:n//2]
arr2=arr[n//2:]
arr=[]
#print(arr,arr1,arr2)
i1=n//2-1
i2=n-i1-2
while (i1!=-1 and i2!=-1):
arr.append(arr1[i1])
arr.append(arr2[i2])
i1-=1
i2-=1
if(i1!=-1):
arr.append(arr1[i1])
elif(i2!=-1):
arr.append(arr2[i2])
s=""
for i in range(n-1):
if(abs(arr[i]-arr[i+1])==1):
s=-1
print("No answer")
break
else:
s+=chr(arr[i]+96)
if(s!=-1):
s+=chr(arr[-1]+96)
print(s)
#n=0"""
def he(i):
return abs(int(i))
n=int(input())
arr=list(map(he,input().split(" ")))
arr.sort()
ans=0
j=1
i=0
while i<n and j<n:
if(i<j):
if(2*arr[i]>=arr[j]):
ans+=j-i
j+=1
else:
i+=1
if(i==j):
j+=1
print(ans)
``` | output | 1 | 11,667 | 23 | 23,335 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland. | instruction | 0 | 11,668 | 23 | 23,336 |
Tags: binary search, sortings, two pointers
Correct Solution:
```
n = int(input())
a = [abs(int(i)) for i in input().split()]
a.sort()
y = 0
x = 0
ans = 0
while x < n:
while y < n - 1 and a[x] * 2 >= a[y + 1]:
y += 1
ans += y - x
x += 1
print(ans)
``` | output | 1 | 11,668 | 23 | 23,337 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland. | instruction | 0 | 11,669 | 23 | 23,338 |
Tags: binary search, sortings, two pointers
Correct Solution:
```
import bisect
import decimal
from decimal import Decimal
import os
from collections import Counter
import bisect
from collections import defaultdict
import math
import random
import heapq
from math import sqrt
import sys
from functools import reduce, cmp_to_key
from collections import deque
import threading
from itertools import combinations
from io import BytesIO, IOBase
from itertools import accumulate
# sys.setrecursionlimit(200000)
# mod = 10**9+7
# mod = 998244353
decimal.getcontext().prec = 46
def primeFactors(n):
prime = set()
while n % 2 == 0:
prime.add(2)
n = n//2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
prime.add(i)
n = n//i
if n > 2:
prime.add(n)
return list(prime)
def getFactors(n) :
factors = []
i = 1
while i <= math.sqrt(n):
if (n % i == 0) :
if (n // i == i) :
factors.append(i)
else :
factors.append(i)
factors.append(n//i)
i = i + 1
return factors
def SieveOfEratosthenes(n):
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
num = []
for p in range(2, n+1):
if prime[p]:
num.append(p)
return num
def lcm(a,b):
return (a*b)//math.gcd(a,b)
def sort_dict(key_value):
return sorted(key_value.items(), key = lambda kv:(kv[1], kv[0]))
def list_input():
return list(map(int,input().split()))
def num_input():
return map(int,input().split())
def string_list():
return list(input())
def decimalToBinary(n):
return bin(n).replace("0b", "")
def binaryToDecimal(n):
return int(n,2)
def DFS(n,s,adj):
visited = [False for i in range(n+1)]
stack = []
stack.append(s)
while (len(stack)):
s = stack[-1]
stack.pop()
if (not visited[s]):
visited[s] = True
for node in adj[s]:
if (not visited[node]):
stack.append(node)
def solve():
n = int(input())
arr = []
for i in list_input():
arr.append(abs(i))
arr.sort()
brr = []
for i in arr:
brr.append(math.ceil(i/2))
pairs = 0
i = n-1
while i >= 0:
arr.pop()
indx = bisect.bisect_left(arr,brr[i])
pairs += (len(arr)-indx)
i -= 1
print(pairs)
t = 1
#t = int(input())
for _ in range(t):
solve()
``` | output | 1 | 11,669 | 23 | 23,339 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland. | instruction | 0 | 11,670 | 23 | 23,340 |
Tags: binary search, sortings, two pointers
Correct Solution:
```
N = int(input())
List = sorted([abs(int(i)) for i in input().split()])
l = len(List) - 2
r = len(List) - 1
answer = 0
while(l > -1):
while( 2*List[l] >= List[r] and l > -1):
l -= 1
if(l >= 0):
answer += (r-1-l)
r -= 1
if(l == -1):
answer += (r)*(r+1)/2
break
print(int(answer))
``` | output | 1 | 11,670 | 23 | 23,341 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland. | instruction | 0 | 11,671 | 23 | 23,342 |
Tags: binary search, sortings, two pointers
Correct Solution:
```
from bisect import bisect
N=int(input())
s=[int(x) for x in input().split()]
ans=0
for i in range(0,len(s)):
s[i]=abs(s[i])
L=sorted(s)
for i in range(0,len(L)):
t=bisect(L,2*L[i])
ans=ans+t-i-1
print(ans)
``` | output | 1 | 11,671 | 23 | 23,343 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland. | instruction | 0 | 11,672 | 23 | 23,344 |
Tags: binary search, sortings, two pointers
Correct Solution:
```
import bisect
n=int(input())
l=[abs(int(x)) for x in input().split()]
l.sort()
res=0
for i in range(n-1):
b=bisect.bisect_right(l,2*l[i],i+1)
res+=b-i-1
print(res)
``` | output | 1 | 11,672 | 23 | 23,345 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland. | instruction | 0 | 11,673 | 23 | 23,346 |
Tags: binary search, sortings, two pointers
Correct Solution:
```
import bisect
n=int(input(''))
a=list(map(int, input().split()))
for i in range(n):
if a[i]<0:
a[i]=a[i]*-1
a.sort()
cnt=0
for i in range(n):
if a[i]==0:
cnt+= 0
else:
t=bisect.bisect_left(a, (2*a[i])+1)-1
cnt+=t-i
print(cnt)
``` | output | 1 | 11,673 | 23 | 23,347 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland.
Submitted Solution:
```
from collections import deque
n = int(input().strip())
nums = list(map(int, input().strip().split()))
nums = sorted([abs(num) for num in nums], reverse=True)
res = 0
max_index = 0
curr_index = 1
for curr_index in range(1, n):
while nums[curr_index] * 2 < nums[max_index]:
max_index += 1
res += curr_index - max_index
print(res)
``` | instruction | 0 | 11,674 | 23 | 23,348 |
Yes | output | 1 | 11,674 | 23 | 23,349 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland.
Submitted Solution:
```
# AC
import sys
class Main:
def __init__(self):
self.buff = None
self.index = 0
def next(self):
if self.buff is None or self.index == len(self.buff):
self.buff = self.next_line()
self.index = 0
val = self.buff[self.index]
self.index += 1
return val
def next_line(self):
return sys.stdin.readline().split()
def next_ints(self):
return [int(x) for x in sys.stdin.readline().split()]
def next_int(self):
return int(self.next())
def solve(self):
k = self.next_int()
x = sorted(abs(x) for x in self.next_ints())
i = 0
r = 0
for j in range(k):
while x[j] - x[i] > x[i]:
i += 1
r += j - i
print(r)
if __name__ == '__main__':
Main().solve()
``` | instruction | 0 | 11,675 | 23 | 23,350 |
Yes | output | 1 | 11,675 | 23 | 23,351 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland.
Submitted Solution:
```
import sys
import math
from bisect import bisect_right as br
def int_arr(): return list(map(int, sys.stdin.readline().split()))
def str_arr(): return list(map(str, sys.stdin.readline().split()))
def input(): return sys.stdin.readline().strip()
n=int(input())
arr=int_arr()
for i in range(n):
if arr[i]<0:
arr[i]=arr[i]*(-1)
arr.sort()
ans=0
for i in range(n):
x=arr[i]*2
ind=br(arr,x,i+1)
ans+=(ind-1-i)
print(ans)
``` | instruction | 0 | 11,676 | 23 | 23,352 |
Yes | output | 1 | 11,676 | 23 | 23,353 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland.
Submitted Solution:
```
n=input()
a=sorted(map(abs,map(int,input().split())))
r=i=j=0
while i<len(a):
while 2*a[j]<a[i]:
j+=1
r+=i-j
i+=1
print(r)
``` | instruction | 0 | 11,677 | 23 | 23,354 |
Yes | output | 1 | 11,677 | 23 | 23,355 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland.
Submitted Solution:
```
from functools import lru_cache
import collections
import math
N = int(input())
arr = list(map(int, input("").split()))
arr = [abs(a) for a in arr if a != 0]
arr = sorted(arr)
N = len(arr)
ans = 0
idx = 1
i = 0
while i < N:
if arr[i] * 2 >= arr[idx]:
ans += i - idx
idx += 1
else:
i += 1
if idx >= N:
break
# if arr[i] < 0:
# ans += presum[arr[i] // 2] - presum[arr[i]]
# ans += presum[abs(arr[i]) * 2] - presum[math.ceil(abs(arr[i]) / 2) - 1]
# else:
# ans += presum[abs(arr[i]) * 2] - presum[abs(arr[i])]
print(ans)
``` | instruction | 0 | 11,678 | 23 | 23,356 |
No | output | 1 | 11,678 | 23 | 23,357 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland.
Submitted Solution:
```
n=int(input())
a=list(map(int, input().split()))
for i in range(n):
a[i]=abs(a[i])
a.sort()
l=0
r=n-1
ans=0
while(l<r):
if 2*a[l]>=a[r]:
ans+=(r-l)
l+=1
else:
r-=1
print(2*ans)
``` | instruction | 0 | 11,679 | 23 | 23,358 |
No | output | 1 | 11,679 | 23 | 23,359 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland.
Submitted Solution:
```
from bisect import bisect_left
def f(n, arr):
ans = 0
for i,val in enumerate(arr):
j = bisect_left(arr, val*2)
j = j if j != n else n-1
ans += j-i
return ans
def main():
n = int(input())
arr = sorted(list(map(lambda x: abs(int(x)), input().split())))
print(f(n, arr))
if __name__ == '__main__':
main()
``` | instruction | 0 | 11,680 | 23 | 23,360 |
No | output | 1 | 11,680 | 23 | 23,361 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
Here |z| denotes the absolute value of z.
Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
Input
The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
Output
Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
Examples
Input
3
2 5 -3
Output
2
Input
2
3 6
Output
1
Note
Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
<image>
The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
<image>
As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
<image>
Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland.
Submitted Solution:
```
from sys import stdin,stdout
from itertools import combinations
from collections import defaultdict,OrderedDict,Counter
import math
def listIn():
return list((map(int,stdin.readline().strip().split())))
def stringListIn():
return([x for x in stdin.readline().split()])
def intIn():
return (int(stdin.readline()))
def stringIn():
return (stdin.readline().strip())
if __name__=="__main__":
n=intIn()
a=listIn()
a=[abs(x) for x in a]
a.sort()
count=Counter(a)
b=sorted(set(a))
l=len(b)
arr=[0]*l
for i in range(l):
c=0
for j in range(i+1,l):
if b[j]<=2*b[i]:
#print(b[j],b[i])
arr[i] +=count[b[j]]
else:
break
total=0
#print(arr)
for i in range(l):
total+=count[b[i]]*arr[i]
print(total)
``` | instruction | 0 | 11,681 | 23 | 23,362 |
No | output | 1 | 11,681 | 23 | 23,363 |
Provide a correct Python 3 solution for this coding contest problem.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0 | instruction | 0 | 12,283 | 23 | 24,566 |
"Correct Solution:
```
from itertools import combinations
n = int(input())
l = list(map(int,input().split()))
c = combinations(l,3)
ans=0
for (a,b,c) in c:
if a+b>c and b+c>a and c+a>b and a!=b and b!=c and a!=c:
ans+=1
print(ans)
``` | output | 1 | 12,283 | 23 | 24,567 |
Provide a correct Python 3 solution for this coding contest problem.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0 | instruction | 0 | 12,284 | 23 | 24,568 |
"Correct Solution:
```
n = int(input())
L = sorted(list(map(int,input().split())),reverse = True)
ans = 0
for i in L:
for j in L:
for k in L:
if i<j<k:
if i + j>k:
ans += 1
print(ans)
``` | output | 1 | 12,284 | 23 | 24,569 |
Provide a correct Python 3 solution for this coding contest problem.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0 | instruction | 0 | 12,285 | 23 | 24,570 |
"Correct Solution:
```
from itertools import *
n=int(input())
a=list(map(int,input().split()))
a.sort()
ans=0
for i,j,k in combinations(a,3):
if i<j<k and i+j>k:
ans+=1
print(ans)
``` | output | 1 | 12,285 | 23 | 24,571 |
Provide a correct Python 3 solution for this coding contest problem.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0 | instruction | 0 | 12,286 | 23 | 24,572 |
"Correct Solution:
```
import itertools
n=int(input())
l=list(map(int,input().split()))
cnt=0
for a,b,c in itertools.combinations(l,3):
if a!=b and b!=c and c!=a and abs(b-c)<a and a<b+c :
cnt+=1
print(cnt)
``` | output | 1 | 12,286 | 23 | 24,573 |
Provide a correct Python 3 solution for this coding contest problem.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0 | instruction | 0 | 12,287 | 23 | 24,574 |
"Correct Solution:
```
n = int(input())
listL = list(map(int, input().split()))
count = 0
for l1 in listL:
for l2 in listL:
for l3 in listL:
if l2 > l1 and l3 > l2 and l1+l2 > l3:
count+=1
print(count)
``` | output | 1 | 12,287 | 23 | 24,575 |
Provide a correct Python 3 solution for this coding contest problem.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0 | instruction | 0 | 12,288 | 23 | 24,576 |
"Correct Solution:
```
n=int(input())
l=list(map(int, input().split()))
l.sort()
ans=0
for i in range(n):
for j in range(i+1,n):
for k in range(j+1,n):
if l[i]+l[j]>l[k] and l[i]!=l[j] and l[j]!=l[k]:
ans+=1
print(ans)
``` | output | 1 | 12,288 | 23 | 24,577 |
Provide a correct Python 3 solution for this coding contest problem.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0 | instruction | 0 | 12,289 | 23 | 24,578 |
"Correct Solution:
```
from itertools import combinations
n = int(input())
l = map(int, input().split())
count = 0
for i in combinations(l, 3):
c = sorted(set(i))
if len(c) == 3:
if c[0] + c[1] > c[2]:
count += 1
print(count)
``` | output | 1 | 12,289 | 23 | 24,579 |
Provide a correct Python 3 solution for this coding contest problem.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0 | instruction | 0 | 12,290 | 23 | 24,580 |
"Correct Solution:
```
n=int(input())
Ns=list(map(int, input().split() ) )
ans=0
for i in range(n):
for j in range(i,n):
for k in range(j,n):
a , b , c = sorted([Ns[i] , Ns[j] , Ns[k]])
if a+b>c and a!=b and b!=c:
ans+=1
print(ans)
``` | output | 1 | 12,290 | 23 | 24,581 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0
Submitted Solution:
```
from itertools import combinations as ic
N = int(input())
L = map(int, input().split())
A = list(ic(L, 3))
ans = 0
for i in A:
if 2 * max(i) - sum(i) < 0 and len(set(i)) == 3:
ans += 1
else:
print(ans)
``` | instruction | 0 | 12,291 | 23 | 24,582 |
Yes | output | 1 | 12,291 | 23 | 24,583 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0
Submitted Solution:
```
N = int(input())
A = list(map(int,input().split()))
A.sort()
cnt = 0
for i in range(0,N):
for j in range(i+1,N):
for k in range(j+1,N):
if (A[i]!=A[j]!=A[k]):
if (A[i]+A[j])>A[k]:
cnt+=1
print(cnt)
``` | instruction | 0 | 12,292 | 23 | 24,584 |
Yes | output | 1 | 12,292 | 23 | 24,585 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0
Submitted Solution:
```
import itertools
n = int(input())
a = list(map(int, input().split()))
a.sort()
cnt = 0
for v in itertools.combinations(a, 3):
x, y, z = v[0], v[1], v[2]
if x + y > z and x != y and y != z and z != x:
cnt += 1
print(cnt)
``` | instruction | 0 | 12,293 | 23 | 24,586 |
Yes | output | 1 | 12,293 | 23 | 24,587 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0
Submitted Solution:
```
from itertools import combinations
n = int(input())
l = list(map(int,input().split()))
c = combinations(l,3)
k=0
for (a,b,c) in c:
if a+b>c and b+c>a and c+a>b and a!=b and b!=c and a!=c:
k+=1
print(k)
``` | instruction | 0 | 12,294 | 23 | 24,588 |
Yes | output | 1 | 12,294 | 23 | 24,589 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0
Submitted Solution:
```
n = int(input())
l = list(map(int, input().split()))
l.sort(reverse=True)
ans = 0
for k in range(0, n-2):
for j in range(k+1, n-1):
if l[k]/2 > l[j]:
break
for i in range(j+1, n):
if l[k] > l[j] + l[i]:
continue
else:
ans += 1
print(ans)
``` | instruction | 0 | 12,295 | 23 | 24,590 |
No | output | 1 | 12,295 | 23 | 24,591 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0
Submitted Solution:
```
N=int(input())
L=list(map(int,input().split()))
count=0
for i in range(N):
for j in range(i+1,N):
for k in range(j+1,N):
if L[i]!=L[j]!=L[k]:
sum_=L[i]+L[j]+L[k]
if max(L[i],L[j],L[k])*2<sum_:
count+=1
print(count)
``` | instruction | 0 | 12,296 | 23 | 24,592 |
No | output | 1 | 12,296 | 23 | 24,593 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0
Submitted Solution:
```
N=int(input())
L=list(map(int, input().split()))
count=0
for i in range(N):
for j in range(i+1,N):
for k in range(j+1,N):
L2=[L[i],L[j],L[k]]
L2.sort()
print(L2)
if L2[0]+L2[1]>L2[2] and L2[0] != L2[1] and L2[1] != L2[2] and L2[2] != L2[0]:
count+=1
print(count)
``` | instruction | 0 | 12,297 | 23 | 24,594 |
No | output | 1 | 12,297 | 23 | 24,595 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.
In how many ways can we choose three of the sticks with different lengths that can form a triangle?
That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:
* L_i, L_j, and L_k are all different.
* There exists a triangle whose sides have lengths L_i, L_j, and L_k.
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 L_2 \cdots L_N
Output
Print the number of ways to choose three of the sticks with different lengths that can form a triangle.
Examples
Input
5
4 4 9 7 5
Output
5
Input
6
4 5 4 3 3 5
Output
8
Input
10
9 4 6 1 9 6 10 6 6 8
Output
39
Input
2
1 1
Output
0
Submitted Solution:
```
N = int(input())
L = list(map(int, input().split()))
L.sort()
cnt = 0
for i in range(N):
Li = L[i]
for j in range(N):
Lj = L[j]
if Li != Lj:
for k in range(N):
Lk = L[k]
if Lk != Lj and Lk != Li:
if Lk < Li + Lj:
cnt += 1
print(cnt)
``` | instruction | 0 | 12,298 | 23 | 24,596 |
No | output | 1 | 12,298 | 23 | 24,597 |
Provide a correct Python 3 solution for this coding contest problem.
We have a square grid with N rows and M columns. Takahashi will write an integer in each of the squares, as follows:
* First, write 0 in every square.
* For each i=1,2,...,N, choose an integer k_i (0\leq k_i\leq M), and add 1 to each of the leftmost k_i squares in the i-th row.
* For each j=1,2,...,M, choose an integer l_j (0\leq l_j\leq N), and add 1 to each of the topmost l_j squares in the j-th column.
Now we have a grid where each square contains 0, 1, or 2. Find the number of different grids that can be made this way, modulo 998244353. We consider two grids different when there exists a square with different integers.
Constraints
* 1 \leq N,M \leq 5\times 10^5
* N and M are integers.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of different grids that can be made, modulo 998244353.
Examples
Input
1 2
Output
8
Input
2 3
Output
234
Input
10 7
Output
995651918
Input
314159 265358
Output
70273732 | instruction | 0 | 12,331 | 23 | 24,662 |
"Correct Solution:
```
N, M = map(int, input().split())
mod = 998244353
if N > M:
N, M = M, N
fact = [0] * (M + 1)
powm = [0] * (M + 1)
pown = [0] * (M + 1)
fact[0] = 1
powm[0] = 1
pown[0] = 1
for i in range(1, M + 1):
fact[i] = fact[i - 1] * i % mod
powm[i] = powm[i - 1] * (M + 1) % mod
pown[i] = pown[i - 1] * (N + 1) % mod
def pow(n, m):
if m == 0:
return 1
elif m == 1:
return n
elif m % 2 == 0:
return pow(n, m // 2)**2 % mod
else:
return pow(n, m // 2)**2 % mod * n % mod
inv_fact = [0] * (M + 1)
inv_fact[M] = pow(fact[M], mod-2)
for i in reversed(range(0, M)):
inv_fact[i] = inv_fact[i + 1] * (i + 1) % mod
def C(n, r):
return fact[n] * inv_fact[r] % mod * inv_fact[n - r] % mod
ans = 0
for i in range(N+1):
ans += (-1)**i * C(N, i) * C(M, i) * fact[i] * powm[N - i] * pown[M - i]
ans = ans % mod
print(ans)
``` | output | 1 | 12,331 | 23 | 24,663 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The math faculty of Berland State University has suffered the sudden drop in the math skills of enrolling students. This year the highest grade on the entrance math test was 8. Out of 100! Thus, the decision was made to make the test easier.
Future students will be asked just a single question. They are given a sequence of integer numbers a_1, a_2, ..., a_n, each number is from 1 to 3 and a_i ≠ a_{i + 1} for each valid i. The i-th number represents a type of the i-th figure:
1. circle;
2. isosceles triangle with the length of height equal to the length of base;
3. square.
The figures of the given sequence are placed somewhere on a Cartesian plane in such a way that:
* (i + 1)-th figure is inscribed into the i-th one;
* each triangle base is parallel to OX;
* the triangle is oriented in such a way that the vertex opposite to its base is at the top;
* each square sides are parallel to the axes;
* for each i from 2 to n figure i has the maximum possible length of side for triangle and square and maximum radius for circle.
Note that the construction is unique for some fixed position and size of just the first figure.
The task is to calculate the number of distinct points (not necessarily with integer coordinates) where figures touch. The trick is, however, that the number is sometimes infinite. But that won't make the task difficult for you, will it?
So can you pass the math test and enroll into Berland State University?
Input
The first line contains a single integer n (2 ≤ n ≤ 100) — the number of figures.
The second line contains n integer numbers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 3, a_i ≠ a_{i + 1}) — types of the figures.
Output
The first line should contain either the word "Infinite" if the number of distinct points where figures touch is infinite or "Finite" otherwise.
If the number is finite than print it in the second line. It's guaranteed that the number fits into 32-bit integer type.
Examples
Input
3
2 1 3
Output
Finite
7
Input
3
1 2 3
Output
Infinite
Note
Here are the glorious pictures for the examples. Note that the triangle is not equilateral but just isosceles with the length of height equal to the length of base. Thus it fits into a square in a unique way.
The distinct points where figures touch are marked red.
In the second example the triangle and the square touch each other for the whole segment, it contains infinite number of points.
<image> | instruction | 0 | 12,505 | 23 | 25,010 |
Tags: geometry
Correct Solution:
```
"""for p in range(int(input())):
n,k=map(int,input().split(" "))
number=input().split(" ")
chances=[k for i in range(n)]
prev=-1
prev_updated=-1
last_used=False
toSub=0
start=0
prevSub=0
if(number[0]=='1'):
prev=0
prev_updated=0
start=1
for i in range(start,n):
if(number[i]=='1'):
# print("\ni",i,"\ntoSub",toSub,"\nprevUpadted",prev_updated,"\nprev",prev,"\nlast_used",last_used)
f1=False
# toSub+=1
toSub=0
zeros=i - prev_updated - 1
if(last_used):
zeros-=1
#chances[i]-=toSub
#print(prevSub,(i - prev - 1 ) +1)
if(i - prev - 1 <= prevSub):
chances[i]-= prevSub - (i - prev - 1 ) +1
if(chances[i]<zeros):
chances[i]=zeros
toSub+= prevSub - (i - prev - 1 ) +1
f1=True
if(zeros==0 or chances[i]==0):
prev_updated=i
prev=i
last_used=False
prevSub=toSub
continue
# print("\nchances: ",chances[i],"\t\tzeroes : ",zeros,"\t\tprevSub :",prevSub)
if(chances[i]>zeros):
# print("\t\t\t\t1")
number[i-zeros]='1'
number[i]='0'
prev_updated=i-zeros
last_used=False
elif(chances[i]==zeros):
# print("\t\t\t\t2")
number[i]='0'
number[i-chances[i]]='1'
prev_updated=i-chances[i]
last_used=True
else:
# print("\t\t\t\t3")
number[i]='0'
number[i-chances[i]]='1'
prev_updated=i-chances[i]
last_used=True
prev=i
prevSub=toSub
if(prev_updated>2 and f1):
if(number[prev_updated]=='1' and number[prev_updated-1]=='0' and number[prev_updated-2]=='1'):
last_used=False
#if()
# print("\ni",i,"\ntoSub",toSub,"\nprevUpadted",prev_updated,"\nprev",prev,"\nlast_used",last_used)
# print(number)
else:
toSub=0
print(*number)
# print(chances)"""
"""class offer:
def __init__(self, n, fre):
self.num = n
self.free = fre
self.delta= n-fre
n,m,k=map(int,input().split(" "))
shovel=list(map(int,input().split(" ")))
#dicti={}
offers=[]
temp_arr=[False for i in range(n)]
for i in range(m):
p,q=map(int,input().split(" "))
if(p>k):
continue
offers.append(offer(p,q))
# dicti[p]=q
#for i in dicti:
# dicti[i].sort()
shovel.sort()
shovel=shovel[:k+1]
offers.sort(key=lambda x: x.delta/x.num,reverse=True)
bestoffer=[]
for i in offers:
if(not temp_arr[i.num]):
temp_arr[i.num]=True
bestoffer.append(i)
cost=0
for i in bestoffer:
"""
"""
n=int(input())
arr=list(map(int,input().split(" ")))
ans=0
for i in range(n-1):
print(ans)
if(((arr[i]==2 and arr[i+1]==3) or (arr[i]==3 and arr[i+1]==2))):
print("Infinite")
ans=-100
break
else:
if(((arr[i]==1 and arr[i+1]==3) or (arr[i]==3 and arr[i+1]==1))):
ans+=4
elif(((arr[i]==1 and arr[i+1]==2) or (arr[i]==2 and arr[i+1]==1))):
ans+=3
if(ans>0):
print("Finite")
print(ans)
#for p in range(1):
for p in range(int(input())):
arr=list(input())
n=len(arr)
for i in range(n):
arr[i]=ord(arr[i])-96
arr.sort()
arr1=arr[:n//2]
arr2=arr[n//2:]
arr=[]
#print(arr,arr1,arr2)
i1=n//2-1
i2=n-i1-2
while (i1!=-1 and i2!=-1):
arr.append(arr1[i1])
arr.append(arr2[i2])
i1-=1
i2-=1
if(i1!=-1):
arr.append(arr1[i1])
elif(i2!=-1):
arr.append(arr2[i2])
#print(arr)
s=""
for i in range(n-1):
if(abs(arr[i]-arr[i+1])==1):
s=-1
print("No answer")
break
else:
s+=chr(arr[i]+96)
if(s!=-1):
s+=chr(arr[-1]+96)
print(s)"""
"""
n,m=map(int,input().split(" "))
seti=[]
ans=[1 for i in range(n)]
for i in range(m):
arr=list(map(int,input().split(" ")))
if(arr[0]>1):
seti.append(set(arr[1:]))
else:
m-=1
parent=[-1 for i in range(m)]
#print(seti)
for i in range(m-1):
for j in range(i+1,m):
if(parent[j]==-1):
if(len(seti[i].intersection(seti[j]))>0):
seti[i]=seti[i].union(seti[j])
parent[j]=i
#print(parent)
for i in range(m):
if(parent[i]==-1):
temp=list(seti[i])
store=len(temp)
for j in temp:
ans[j-1]=store
print(*ans)"""
n=int(input())
temp=input()
arr=list(map(int,temp.split(" ")))
wrong=False
for i in range(1,n):
if(arr[i-1]*arr[i]==6):
print("Infinite")
wrong=True
break
ans=0
if(not wrong):
for j in range(1,n):
if(arr[j-1]*arr[j]==2):
ans+=3
elif(arr[j-1]*arr[j]==3):
ans+=4
print("Finite")
print(ans-temp.count("3 1 2"))
``` | output | 1 | 12,505 | 23 | 25,011 |
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