message stringlengths 2 44.5k | message_type stringclasses 2
values | message_id int64 0 1 | conversation_id int64 42 109k | cluster float64 5 5 | __index_level_0__ int64 84 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a consisting of n integers. Find the maximum possible value of <image> (integer remainder of ai divided by aj), where 1 ≤ i, j ≤ n and ai ≥ aj.
Input
The first line contains integer n — the length of the sequence (1 ≤ n ≤ 2·105).
The second line contains n space-separated integers ai (1 ≤ ai ≤ 106).
Output
Print the answer to the problem.
Examples
Input
3
3 4 5
Output
2
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
b = a[:]
a.sort()
max = 0
for i in reversed(range(1,n)):
for j in reversed(range(n-1)):
if a[j]<b[i]:
if max<b[i]%a[j]:
max = a[i]%b[j]
else:
break
print(max)
``` | instruction | 0 | 24,228 | 5 | 48,456 |
No | output | 1 | 24,228 | 5 | 48,457 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a consisting of n integers. Find the maximum possible value of <image> (integer remainder of ai divided by aj), where 1 ≤ i, j ≤ n and ai ≥ aj.
Input
The first line contains integer n — the length of the sequence (1 ≤ n ≤ 2·105).
The second line contains n space-separated integers ai (1 ≤ ai ≤ 106).
Output
Print the answer to the problem.
Examples
Input
3
3 4 5
Output
2
Submitted Solution:
```
def read():
listA = []
inputA = input()
inputB = input()
inputB = inputB.split()
listA.append(int(inputA))
for i in range(len(inputB)):
listA.append(int(inputB[i]))
return listA
def max_val(l):
n = int(l[0])
l.pop(0)
l = sorted(l)
aj = []
largest = 0
for i in range(n):
if l[i] not in aj:
aj.append(l[i])
for i in range(len(aj)):
for j in range(len(l)):
if ((l[i] / 2)+1) < aj[i]:
pass
else:
if l[j] > aj[i]:
haha = l[j] % aj[i]
if haha > largest:
largest = haha
else:
pass
return largest
print(max_val(read()))
``` | instruction | 0 | 24,229 | 5 | 48,458 |
No | output | 1 | 24,229 | 5 | 48,459 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a consisting of n integers. Find the maximum possible value of <image> (integer remainder of ai divided by aj), where 1 ≤ i, j ≤ n and ai ≥ aj.
Input
The first line contains integer n — the length of the sequence (1 ≤ n ≤ 2·105).
The second line contains n space-separated integers ai (1 ≤ ai ≤ 106).
Output
Print the answer to the problem.
Examples
Input
3
3 4 5
Output
2
Submitted Solution:
```
n=int(input())
dp=list(map(int,input().split()))
re=[0]*n
for i in range(n-1,-1,-1):
j=i+1
mx=0
while j<n:
t=dp[j]%dp[i]
if t==0:
mx=max(mx,re[j])
break
else:
mx=max(mx,t)
j+=1
re[i]=mx
print(max(re))
``` | instruction | 0 | 24,230 | 5 | 48,460 |
No | output | 1 | 24,230 | 5 | 48,461 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a consisting of n integers. Find the maximum possible value of <image> (integer remainder of ai divided by aj), where 1 ≤ i, j ≤ n and ai ≥ aj.
Input
The first line contains integer n — the length of the sequence (1 ≤ n ≤ 2·105).
The second line contains n space-separated integers ai (1 ≤ ai ≤ 106).
Output
Print the answer to the problem.
Examples
Input
3
3 4 5
Output
2
Submitted Solution:
```
import math
def findnearestidx(aList,key,limit):
lo = limit
hi = len(aList)
while (lo < hi-1):
mid = (lo+hi)//2
if key >=aList[mid]:
hi = mid
else:
lo = mid
if hi == len(aList):
hi = hi-1
while aList[hi] < key and hi > limit:
hi = hi-1
return hi
def recursivemod(aList,n,limit,k=1,idx=0):
div = n//(k+1) + 1
if n == 1:
return 0
elif div >= limit:
return n%div
else:
idx = findnearestidx(aList,div,idx)
return max(n%aList[idx],recursivemod(aList,n,div-1,k+1,idx))
n = int(input())
a = input()
a = a.split()
for i in range(len(a)):
a[i] = int(a[i])
a.sort(reverse=True)
maxmod = recursivemod(a,a[0],a[0])
i = 1
while i<n and maxmod < (math.ceil(a[i]/2) - 1):
maxmod = max(maxmod,recursivemod(a,a[i],a[i]))
i += 1
print(maxmod)
``` | instruction | 0 | 24,231 | 5 | 48,462 |
No | output | 1 | 24,231 | 5 | 48,463 |
Provide a correct Python 3 solution for this coding contest problem.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000 | instruction | 0 | 24,477 | 5 | 48,954 |
"Correct Solution:
```
a = *map(int, input().split()),
print(max(x * y for x in a[:2] for y in a[2:]))
``` | output | 1 | 24,477 | 5 | 48,955 |
Provide a correct Python 3 solution for this coding contest problem.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000 | instruction | 0 | 24,478 | 5 | 48,956 |
"Correct Solution:
```
a,b,c,d = map(int,input().split(" "))
print(max([a*c,a*d,b*c,b*d]))
``` | output | 1 | 24,478 | 5 | 48,957 |
Provide a correct Python 3 solution for this coding contest problem.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000 | instruction | 0 | 24,479 | 5 | 48,958 |
"Correct Solution:
```
a,b,c,d=[int(r) for r in input().split()]
print(max(a*c,a*d,b*c,b*d))
``` | output | 1 | 24,479 | 5 | 48,959 |
Provide a correct Python 3 solution for this coding contest problem.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000 | instruction | 0 | 24,480 | 5 | 48,960 |
"Correct Solution:
```
a,b,c,d=map(int,input().split())
A=[a*c,b*c,a*d,b*d]
print(max(A))
``` | output | 1 | 24,480 | 5 | 48,961 |
Provide a correct Python 3 solution for this coding contest problem.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000 | instruction | 0 | 24,481 | 5 | 48,962 |
"Correct Solution:
```
a, b, c, d = map(int,input().rstrip().split())
print(max(a*c, a*d, b*c, b*d))
``` | output | 1 | 24,481 | 5 | 48,963 |
Provide a correct Python 3 solution for this coding contest problem.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000 | instruction | 0 | 24,482 | 5 | 48,964 |
"Correct Solution:
```
a,b,c,d=map(int,input().split())
maxa=max(a*c,a*d,b*c,b*d)
print(maxa)
``` | output | 1 | 24,482 | 5 | 48,965 |
Provide a correct Python 3 solution for this coding contest problem.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000 | instruction | 0 | 24,483 | 5 | 48,966 |
"Correct Solution:
```
a,b,c,d = map(int,input().split())
print(int(max(a*c,a*d,b*c,b*d)))
``` | output | 1 | 24,483 | 5 | 48,967 |
Provide a correct Python 3 solution for this coding contest problem.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000 | instruction | 0 | 24,484 | 5 | 48,968 |
"Correct Solution:
```
a,b,c,d = map(int, input().split())
ans = max(a*c, b*c, b*d, a*d)
print(ans)
``` | output | 1 | 24,484 | 5 | 48,969 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000
Submitted Solution:
```
a,b,c,d = list(map(int,input().split()))
print(max(a*c,a*d,b*c,d*b))
``` | instruction | 0 | 24,485 | 5 | 48,970 |
Yes | output | 1 | 24,485 | 5 | 48,971 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000
Submitted Solution:
```
a, b, c, d = list(map(int, input().split()))
print(max(b*d, a*c, a*d, b*c))
``` | instruction | 0 | 24,486 | 5 | 48,972 |
Yes | output | 1 | 24,486 | 5 | 48,973 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000
Submitted Solution:
```
# スペース区切りの整数の入力
a, b, c, d= map(int, input().split())
print(max(a*c,a*d,b*c,b*d))
``` | instruction | 0 | 24,487 | 5 | 48,974 |
Yes | output | 1 | 24,487 | 5 | 48,975 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000
Submitted Solution:
```
a,b,c,d=list(map(int,input().split()))
x=[a*c,a*d,b*c,b*d]
print(max(x))
``` | instruction | 0 | 24,488 | 5 | 48,976 |
Yes | output | 1 | 24,488 | 5 | 48,977 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000
Submitted Solution:
```
a, b, c, d = [int(x) for x in input().split()]
x, y = 0, 0
if a == 0:
a = b
elif b == 0:
b = a
if c == 0:
c = d
elif d == 0:
d = c
if a <= 0 and b <= 0:
y = c
else:
y = d
if c <= 0 and d <= 0:
x = a
else:
x = b
print(x*y)
``` | instruction | 0 | 24,489 | 5 | 48,978 |
No | output | 1 | 24,489 | 5 | 48,979 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000
Submitted Solution:
```
value = [int(i) for i in input().split()]
l = []
if value[0] == value[1] == value[2] == value[3] == 0:
print("0")
elif value[2] < 0 and value[0] < 0:
print(value[0] * value[2])
elif 0 < value[0] < value[1] and value[2] < value[3] < 0:
print(value[0] * value[3])
elif 0 < value[0] < value[1] and 0 < value[1] < value[2]:
print(value[1] * value[3])
else:
print(value[1] * value[2])
``` | instruction | 0 | 24,490 | 5 | 48,980 |
No | output | 1 | 24,490 | 5 | 48,981 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000
Submitted Solution:
```
a,b,c,d=map(int,input().split())
ans=max((a*c),(a*d),(b*c),(b*d))
print(max)
``` | instruction | 0 | 24,491 | 5 | 48,982 |
No | output | 1 | 24,491 | 5 | 48,983 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are integers a,b,c and d. If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?
Constraints
* -10^9 \leq a \leq b \leq 10^9
* -10^9 \leq c \leq d \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
a b c d
Output
Print the answer.
Examples
Input
1 2 1 1
Output
2
Input
3 5 -4 -2
Output
-6
Input
-1000000000 0 -1000000000 0
Output
1000000000000000000
Submitted Solution:
```
a,b,c,d=map(int,input().split())
List=[]
for i in range(a,b+1):
for j in range(c,d+1):
List.append(i*j)
max(List)
``` | instruction | 0 | 24,492 | 5 | 48,984 |
No | output | 1 | 24,492 | 5 | 48,985 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No | instruction | 0 | 24,557 | 5 | 49,114 |
"Correct Solution:
```
from itertools import combinations
n = int(input())
yes = [i*(i-1)//2 for i in range(2, 448)]
if n in yes:
print('Yes')
len_s = yes.index(n) + 1
print(len_s+1)
res = [[] for _ in range(len_s+1)]
for i, v in enumerate(combinations(range(len_s+1), 2)):
res[v[0]].append(str(i+1))
res[v[1]].append(str(i+1))
for r in res:
print(' '.join([str(len_s)] + r))
else:
print('No')
``` | output | 1 | 24,557 | 5 | 49,115 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No | instruction | 0 | 24,558 | 5 | 49,116 |
"Correct Solution:
```
def main():
#部分集合のサイズnの時n+1個の部分集合
n=int(input())
if 2*n!=int((2*n)**0.5)*(int((2*n)**0.5)+1):
print("No")
exit()
print("Yes")
l=int((2*n)**0.5)
print(l+1)
work=[[] for _ in range(l+1)]
now_sub=0
next_sub=1
for i in range(1,n+1):
if len(work[now_sub])==l:
now_sub+=1
next_sub=now_sub+1
work[now_sub].append(i)
work[next_sub].append(i)
next_sub+=1
for i in range(l+1):
print("{} {}".format(l," ".join(map(str,work[i]))))
main()
``` | output | 1 | 24,558 | 5 | 49,117 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No | instruction | 0 | 24,559 | 5 | 49,118 |
"Correct Solution:
```
import sys
readline = sys.stdin.readline
sys.setrecursionlimit(10**8)
mod = 10**9+7
#mod = 998244353
INF = 10**18
eps = 10**-7
N = int(readline())
for i in range(1,1000):
if i*(i-1)//2 == N:
k = i
print('Yes')
break
if i == 999:
print('No')
exit()
print(k)
ans = [[] for i in range(k)]
now = 1
import itertools
L = [i for i in range(k)]
for v in itertools.combinations(L,2):
ans[v[0]].append(now)
ans[v[1]].append(now)
now += 1
for aaa in ans:
print(len(aaa),' '.join(map(str,aaa)))
``` | output | 1 | 24,559 | 5 | 49,119 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No | instruction | 0 | 24,560 | 5 | 49,120 |
"Correct Solution:
```
N = int(input())
ss = [[1], [1]]
n = 2
for i in range(1, N):
l = i + 1
ss = [ss[i] + [n + i] for i in range(l)]
ss += [[n + i for i in range(l)]]
n += l
if n - 1 >= N:
break
if n - 1 == N:
print("Yes")
print(len(ss))
for r in ss:
print(len(r), *r)
else:
print("No")
``` | output | 1 | 24,560 | 5 | 49,121 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No | instruction | 0 | 24,561 | 5 | 49,122 |
"Correct Solution:
```
N = int(input())
flag = 0
for i in range(int((8*N+1)**0.5)+1):
if i*(i-1)==2*N:
flag = 1
k = i
break
if flag==0:
print("No")
else:
print("Yes")
S = [[] for _ in range(k)]
cnt = 1
for i in range(k-1):
for j in range(i+1,k):
S[i].append(cnt)
S[j].append(cnt)
cnt += 1
print(k)
for i in range(k):
print(len(S[i]),*S[i])
``` | output | 1 | 24,561 | 5 | 49,123 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No | instruction | 0 | 24,562 | 5 | 49,124 |
"Correct Solution:
```
import math
N=int(input())
q=int(math.sqrt(N*2))
if N*2!=q*q+q:print("No");exit()
S=[list(range(1,q+1))]
S+=[[j]for j in S[0]]
last=q
for i in range(1,q):
r=list(range(last+1,last+1+q-i))
S[i]+=r
for j in range(q-i):S[i+j+1]+=[r[j]]
last=r[-1]
print("Yes")
print(len(S))
for s in S:print(len(s)," ".join(map(str,s)))
``` | output | 1 | 24,562 | 5 | 49,125 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No | instruction | 0 | 24,563 | 5 | 49,126 |
"Correct Solution:
```
n = int(input())
k = int((n*2)**.5) + 1
if (k - 1) * k / 2 == n:
print('Yes')
print(k)
else:
print('No')
exit()
t = [1] * (k - 1)
for i in range(1, k - 1):
t[i] = t[i-1] + i
for i in range(k-1):
s = (t[max(i, j)] + min(i, j) for j in range(k-1))
print(k-1, *s)
print(k - 1, *(t[j] + j for j in range(k-1)))
``` | output | 1 | 24,563 | 5 | 49,127 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No | instruction | 0 | 24,564 | 5 | 49,128 |
"Correct Solution:
```
N=int(input())
x=1
while x*(x-1)//2<N:
x+=1
if x*(x-1)//2>N:
print('No')
else:
print('Yes')
print(x)
a=[[] for i in range(x)]
from itertools import combinations
y=1
for i,j in combinations(range(x),2):
a[i].append(y)
a[j].append(y)
y+=1
for l in a:
print(x-1,*l)
``` | output | 1 | 24,564 | 5 | 49,129 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No
Submitted Solution:
```
from math import sqrt, ceil
def tostr(a):
return ' '.join(map(str, a))
N = int(input())
k = ceil(sqrt(N*2))
#print(k)
if N!=k*(k-1)/2:
print('No')
exit()
print('Yes')
print(k)
M = k - 1
# diagonal
a = [1]
for i in range(M-1):
a.append(a[-1] + i + 2)
print(M, tostr(a))
#
for i in range(M):
a = [int(i*(i+1)/2) + 1]
a += list(range(a[-1]+1, a[-1]+i+1))
#print(a)
for j in range(i+1, M):
a.append(a[-1] + j)
print(M, tostr(a))
``` | instruction | 0 | 24,565 | 5 | 49,130 |
Yes | output | 1 | 24,565 | 5 | 49,131 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No
Submitted Solution:
```
n = int(input())
a = []
for i in range(1,500):
a.append(i*(i-1)//2)
if (n in a):
print("Yes")
x = a.index(n)+1 #3
ans = [[] for _ in range(x)]
now = 1
l = 0
while l<x:
for i in range(x-l-1):
ans[l].append(now)
ans[l+1+i].append(now)
now += 1
l += 1
print(x)
for i in range(x):
print(x-1,*ans[i])
else:
print("No")
``` | instruction | 0 | 24,566 | 5 | 49,132 |
Yes | output | 1 | 24,566 | 5 | 49,133 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No
Submitted Solution:
```
n = int(input())
for i in range(10 ** 5):
if 2 * n == i ** 2 - i:
k = i
print('Yes', k, sep='\n')
break
elif 2 * n < i ** 2 - i:
print('No')
exit()
num, ans = 1, [[] for _ in range(k)]
for i in range(k):
for j in range(i + 1, k):
ans[i].append(num)
ans[j].append(num)
num += 1
print(k - 1, *ans[i])
``` | instruction | 0 | 24,567 | 5 | 49,134 |
Yes | output | 1 | 24,567 | 5 | 49,135 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No
Submitted Solution:
```
def main():
n=int(input())
m=int((2*n)**0.5)
if m*(m+1)==n*2:
print("Yes")
m+=1
print(m)
else:
print("No")
exit()
ans=[[m-1] for i in range(m)]
c=1
for i in range(m):
for j in range(i+1,m):
ans[i].append(c)
ans[j].append(c)
c+=1
for i in ans:
print(" ".join(map(str,i)))
if __name__ == '__main__':
main()
``` | instruction | 0 | 24,568 | 5 | 49,136 |
Yes | output | 1 | 24,568 | 5 | 49,137 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No
Submitted Solution:
```
n = int(input())
if n != 3:
print('No')
else:
print('Yes')
print(3)
print(2, 1, 2)
print(2, 3, 1)
print(2, 2, 3)
``` | instruction | 0 | 24,569 | 5 | 49,138 |
No | output | 1 | 24,569 | 5 | 49,139 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No
Submitted Solution:
```
def etrc(n1,n2,rs):
for r in range(n1):
rc[n2].append(rs+r)
rc[n2+r+1].append(rs+r)
n=int(input())
x=int(((1+8*n)**0.5-1)/2)
rc=[[] for i in range(x+2)]
if n!=x*(x+1)//2:
print("No")
else:
print("Yes")
print(x+1)
rs=1
for i in range(x+1):
n1=x+1-i
n2=i
etrc(n1,n2,rs)
rs=rs+n1
for i in range(x+2):
print(x+1, end=" ")
for j in range(x+1):
print(rc[i][j], end=" ")
print()
``` | instruction | 0 | 24,570 | 5 | 49,140 |
No | output | 1 | 24,570 | 5 | 49,141 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No
Submitted Solution:
```
#!/usr/bin/env python3
from collections import defaultdict, Counter
from itertools import product, groupby, count, permutations, combinations
from math import pi, sqrt
from collections import deque
from bisect import bisect, bisect_left, bisect_right
from string import ascii_lowercase
from functools import lru_cache
import sys
sys.setrecursionlimit(10000)
INF = float("inf")
YES, Yes, yes, NO, No, no = "YES", "Yes", "yes", "NO", "No", "no"
dy4, dx4 = [0, 1, 0, -1], [1, 0, -1, 0]
dy8, dx8 = [0, -1, 0, 1, 1, -1, -1, 1], [1, 0, -1, 0, 1, 1, -1, -1]
def inside(y, x, H, W):
return 0 <= y < H and 0 <= x < W
def ceil(a, b):
return (a + b - 1) // b
def sum_of_arithmetic_progression(s, d, n):
return n * (2 * s + (n - 1) * d) // 2
def gcd(a, b):
if b == 0:
return a
return gcd(b, a % b)
def lcm(a, b):
g = gcd(a, b)
return a / g * b
def solve(N):
if N == 1:
print(Yes)
print(1, 1)
print(1, 1)
return
K = -1
for k in range(1, N + 1):
if (k * (k - 1)) // 2 == N:
K = k
if K == -1:
print(No)
return
ans = [[] for _ in range(K)]
num = 1
for i in range(0, K):
for j in range(i + 1, K):
ans[i].append(num)
ans[j].append(num)
num += 1
print(Yes)
print(K)
for v in ans:
print(len(v), *v, sep=" ")
def main():
N = int(input())
solve(N)
if __name__ == '__main__':
main()
``` | instruction | 0 | 24,571 | 5 | 49,142 |
No | output | 1 | 24,571 | 5 | 49,143 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer N. Determine if there exists a tuple of subsets of \\{1,2,...N\\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
* Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.
* Any two of the sets S_1,S_2,...,S_k have exactly one element in common.
If such a tuple exists, construct one such tuple.
Constraints
* 1 \leq N \leq 10^5
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
If a tuple of subsets of \\{1,2,...N\\} that satisfies the conditions does not exist, print `No`. If such a tuple exists, print `Yes` first, then print such subsets in the following format:
k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
Examples
Input
3
Output
Yes
3
2 1 2
2 3 1
2 2 3
Input
4
Output
No
Submitted Solution:
```
N = int(input())
n1 = 8*N+1
a = int(n1**0.5)
if N>=3 and n1==a**2:
n = (-3+a)//2
if (-3+a)%2:
print("No")
else:
d = [[0]*(n+1) for _ in range(n+2)]
d[0][0] = 1
d[0][1] = 2
d[1][0] = 2
d[1][1] = 3
d[2][0] = 3
d[2][1] = 1
for i in range(1, n):
v = 4+((i-1)*(i+4)//2)
c = 2+i
for j in range(c):
d[c][j] = v+j
d[j][c-1] = v+j
print("Yes")
print(n+2)
for i in range(n+2):
print(n+1, *d[i], sep=" ")
else:
print("No")
``` | instruction | 0 | 24,572 | 5 | 49,144 |
No | output | 1 | 24,572 | 5 | 49,145 |
Provide a correct Python 3 solution for this coding contest problem.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0 | instruction | 0 | 24,573 | 5 | 49,146 |
"Correct Solution:
```
n=int(input())
a=list(map(int, input().split()))
b=max(a)
_,c=min([(abs(b/2-x), x) for x in a])
print("%d %d" % (b, c))
``` | output | 1 | 24,573 | 5 | 49,147 |
Provide a correct Python 3 solution for this coding contest problem.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0 | instruction | 0 | 24,574 | 5 | 49,148 |
"Correct Solution:
```
n=int(input())
a=[int(i) for i in input().split()]
m=max(a)
m2 = m / 2
f = m
ans = -m
for i in a:
if i != m and abs(m2 - i) <=f:
f = abs(m2 - i)
ans = i
print(m,ans)
``` | output | 1 | 24,574 | 5 | 49,149 |
Provide a correct Python 3 solution for this coding contest problem.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0 | instruction | 0 | 24,575 | 5 | 49,150 |
"Correct Solution:
```
N, *A = map(int, open(0).read().split())
A.sort()
x = [abs(A[-1] - 2 * A[i]) for i in range(N - 1)]
y = sorted((v, i) for i, v in enumerate(x))
print(A[-1], A[y[0][1]])
``` | output | 1 | 24,575 | 5 | 49,151 |
Provide a correct Python 3 solution for this coding contest problem.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0 | instruction | 0 | 24,576 | 5 | 49,152 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
m = max(a)
ans = ' '.join((
str(m),
str(max(sorted(a), key=lambda x: min(x, m - x)))
))
print(ans)
``` | output | 1 | 24,576 | 5 | 49,153 |
Provide a correct Python 3 solution for this coding contest problem.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0 | instruction | 0 | 24,577 | 5 | 49,154 |
"Correct Solution:
```
N = int(input())
A = sorted(list(map(int,input().split())))
B = A[-1]
print(B,min(A,key=lambda x: abs(B-2*x)))
``` | output | 1 | 24,577 | 5 | 49,155 |
Provide a correct Python 3 solution for this coding contest problem.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0 | instruction | 0 | 24,578 | 5 | 49,156 |
"Correct Solution:
```
n=int(input())
a=sorted(map(int,input().split()))
ans=a[-1]
m=float('inf')
k=0
for i in range(n):
if abs(ans/2-a[i])<m:
m=abs(ans/2-a[i])
k=i
print(ans,a[k])
``` | output | 1 | 24,578 | 5 | 49,157 |
Provide a correct Python 3 solution for this coding contest problem.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0 | instruction | 0 | 24,579 | 5 | 49,158 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
N = max(a)
a.remove(N)
li = [abs(N/2 - k) for k in a]
index = li.index(min(li))
print("{0} {1}".format(N, a[index]))
``` | output | 1 | 24,579 | 5 | 49,159 |
Provide a correct Python 3 solution for this coding contest problem.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0 | instruction | 0 | 24,580 | 5 | 49,160 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
a_sorted = sorted(a)
i = max(a_sorted)
j = min(a_sorted, key = lambda x:abs(i - 2 * x))
print(i, j)
``` | output | 1 | 24,580 | 5 | 49,161 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0
Submitted Solution:
```
N = int(input())
A = sorted(list(map(int, input().split())))
a1 = A[-1]
med = (a1+1) // 2
B = [abs(a - med) for a in A]
idx = B.index(min(B))
a2 = A[idx]
print(a1, a2)
``` | instruction | 0 | 24,581 | 5 | 49,162 |
Yes | output | 1 | 24,581 | 5 | 49,163 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0
Submitted Solution:
```
n = input()
a = list(map(int,input().split()))
a.sort()
ma = a[-1]
a = a[:-1]
print(ma,min(a,key=lambda x: abs(ma/2-x)))
``` | instruction | 0 | 24,582 | 5 | 49,164 |
Yes | output | 1 | 24,582 | 5 | 49,165 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0
Submitted Solution:
```
n,l=int(input()),list(map(int,input().split()));l.sort();c=l[-1]/2;a=0
for i in l[:-1]:
if abs(i-c)<abs(a-c):a=i
print(l[-1],a)
``` | instruction | 0 | 24,583 | 5 | 49,166 |
Yes | output | 1 | 24,583 | 5 | 49,167 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0
Submitted Solution:
```
n,*a=map(int,open(0).read().split())
m=max(a)
b=m//2
o=min(a)
for A in a:
if abs(A-b)<abs(o-b):o=A
print(m,o)
``` | instruction | 0 | 24,584 | 5 | 49,168 |
Yes | output | 1 | 24,584 | 5 | 49,169 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0
Submitted Solution:
```
from bisect import bisect_left
n=int(input())
a=list(map(int,input().split()))
a.sort()
maxi=a[-1]
tmp=maxi/2
idx=bisect_left(a,tmp)
if idx==n-1:
idx -=1
print(maxi,a[idx])
``` | instruction | 0 | 24,585 | 5 | 49,170 |
No | output | 1 | 24,585 | 5 | 49,171 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let {\rm comb}(n,r) be the number of ways to choose r objects from among n objects, disregarding order. From n non-negative integers a_1, a_2, ..., a_n, select two numbers a_i > a_j so that {\rm comb}(a_i,a_j) is maximized. If there are multiple pairs that maximize the value, any of them is accepted.
Constraints
* 2 \leq n \leq 10^5
* 0 \leq a_i \leq 10^9
* a_1,a_2,...,a_n are pairwise distinct.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print a_i and a_j that you selected, with a space in between.
Examples
Input
5
6 9 4 2 11
Output
11 6
Input
2
100 0
Output
100 0
Submitted Solution:
```
def comb(n, r):
ans = 1
for i in range(n - r + 1, n + 1):
ans *= i
for i in range(1, r + 1):
ans /= i
return ans
N = int(input())
a = tuple(map(int, input().split()))
n = max(a)
M = 0
for x in a:
if x == n:
continue
res = comb(n, x)
if M < res:
M = res
r = x
print(n, r)
``` | instruction | 0 | 24,586 | 5 | 49,172 |
No | output | 1 | 24,586 | 5 | 49,173 |
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