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.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144
Submitted Solution:
```
#素因数分解、計算量はO(√N)
from collections import defaultdict
def factorize(n):
b = 2
dic = defaultdict(lambda: 0)
while b * b <= n:
while n % b == 0:
n //= b
dic[b] += 1
b = b + 1
if n > 1:
dic[n] += 1
return dic
def extgcd(a, b):
if b:
d, y, x = extgcd(b, a%b)
y -= (a//b)*x
return d, x, y
else:
return a, 1, 0
N = int(input())
fct = factorize(2*N)
lis = []
for k,v in fct.items():
lis.append(pow(k,v))
ans = 10**18
from itertools import groupby, accumulate, product, permutations, combinations
for pro in product([0,1],repeat=len(lis)):
prod1 = 1
for i,p in enumerate(pro):
if p==1:
prod1 *= lis[i]
prod2 = (N*2)//prod1
if min(prod1,prod2)==1:
ans = min(ans, max(prod1,prod2)-1)
else:
d,a1,a2 = extgcd(prod1,prod2)
ans = min(ans, min(abs(a1*prod1),abs(a2*prod2)))
print(ans)
``` | instruction | 0 | 14,769 | 5 | 29,538 |
Yes | output | 1 | 14,769 | 5 | 29,539 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144
Submitted Solution:
```
#dt = {} for i in x: dt[i] = dt.get(i,0)+1
import sys;input = sys.stdin.readline
inp,ip = lambda :int(input()),lambda :[int(w) for w in input().split()]
import math
_1_50 = 1 << 50 # 2**50 == 1,125,899,906,842,624
def isqrt(x):
"""Return the integer part of the square root of x, even for very
large integer values."""
if x < 0:
raise ValueError('square root not defined for negative numbers')
if x < _1_50:
return int(math.sqrt(x)) # use math's sqrt() for small parameters
n = int(x)
if n <= 1:
return n # handle sqrt(0)==0, sqrt(1)==1
# Make a high initial estimate of the result (a little lower is slower!!!)
r = 1 << ((n.bit_length() + 1) >> 1)
while True:
newr = (r + n // r) >> 1 # next estimate by Newton-Raphson
if newr >= r:
return r
r = newr
n = inp()
delta = 8*n
t = 1
from math import sqrt
while True:
t += delta
sq = isqrt(t)
if sq*sq != t:
continue
a = (-1+sq)/2
b = (-1-sq)/2
ans = float('inf')
if a > 0 and a.is_integer():
ans = min(ans,a)
if b > 0 and b.is_integer():
ans = min(ans,b)
if ans != float('inf'):
print(int(ans))
break
``` | instruction | 0 | 14,770 | 5 | 29,540 |
No | output | 1 | 14,770 | 5 | 29,541 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144
Submitted Solution:
```
z=int(input())
def solv_quadratic_equation(a, b, c):
""" 2次方程式を解く """
D = (b**2 - 4*a*c) ** (1/2)
x_1 = (-b + D) / (2 * a)
x_2 = (-b - D) / (2 * a)
return x_1,x_2
ans=0
i=1
# print(10**15)
# a,b=solv_quadratic_equation(1,1,1000000000000000)
# print(a,b)
while True:
a,b=solv_quadratic_equation(1,1,-2*z*i)
if a>=b:
if a.is_integer():
# print(a)
# print(b)
ans=a
break
elif a<=b:
if b.is_integer():
# print(a)
# print(b)
ans=b
break
i+=1
print(int(ans))
``` | instruction | 0 | 14,771 | 5 | 29,542 |
No | output | 1 | 14,771 | 5 | 29,543 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144
Submitted Solution:
```
N=int(input())
i = 1
while True:
k = int((N*2*i)**0.5)
for ik in range(k, k+100):
if ik*(ik+1) == 2*N*i:
print(ik)
exit()
if ik*(ik+1)>2*N*i:
break
i=i+1
``` | instruction | 0 | 14,772 | 5 | 29,544 |
No | output | 1 | 14,772 | 5 | 29,545 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.
Constraints
* 1 \leq N \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer in a line.
Examples
Input
11
Output
10
Input
20200920
Output
1100144
Submitted Solution:
```
n=int(input())
for i in range(int(n**.5)+1,1,-1):
if n % i ==0:
for j in range ( i, n + 1 ):
if (((j * (j + 1))) % (2 * n)) == 0:
print ( j )
exit(0)
else:print(n-1)
``` | instruction | 0 | 14,773 | 5 | 29,546 |
No | output | 1 | 14,773 | 5 | 29,547 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No | instruction | 0 | 14,892 | 5 | 29,784 |
"Correct Solution:
```
# AOJ DSL_2_A "Range Minimum Query"
# SegmantTreeの実装
# 初期化最大値
INF = (1 << 31) - 1
class SegmentTree:
def __init__(self, N):
self.N = 2**(N-1).bit_length()
self.data = [[INF, -1] for _ in range(2*self.N-1)]
# k番目の値(0-indexed)をaに変更
def update(self, k, a):
self.data[k+self.N-1] = [a, k]
k += self.N - 1
while k > 0:
k = (k-1)//2
if self.data[2*k+1][0] < self.data[2*k+2][0]:
self.data[k] = self.data[2*k+1][:]
else:
self.data[k] = self.data[2*k+2][:]
# [l, r)の最小値取得
# kがNodeの番号、対応する区間が[a, b)
def query_min(self, l, r):
L = l + self.N
R = r + self.N
s = [INF, -1]
while L < R:
if R & 1:
R -= 1
if s[0] > self.data[R-1][0]:
s = self.data[R-1]
if L & 1:
if s[0] > self.data[L-1][0]:
s = self.data[L-1]
L += 1
L >>= 1; R >>= 1
return s
import sys
input = sys.stdin.readline
from bisect import bisect_left
N = int(input())
X = list(map(int, input().split()))
sortedX = sorted(X)
decided = [-1]*(N**2+1)
for i, x in enumerate(X):
decided[x] = i+1
marge = SegmentTree(N+1)
remains = [0]*(N+1)
alreadyUsed = [None]*(N+1)
for i, x in enumerate(X):
i += 1
alreadyused = bisect_left(sortedX, x)
if i != 1:
marge.update(i, x-alreadyused-i)
alreadyUsed[i] = alreadyused
remains[i] = i-1
def solve():
offset = 0
for n in range(1,N**2+1):
if decided[n] != -1:
decided_num = decided[n]
if remains[decided_num] > 0:
return False, None
remain = N-decided_num
if remain < 0:
return False, None
if remain == 0:
marge.update(decided_num, INF)
remains[decided_num] = 0
else:
marge_now = (N**2-n)-(N-alreadyUsed[decided_num]-1)-remain+offset
marge.update(decided_num, marge_now)
remains[decided_num] = remain
else:
marge_now, num = marge.query_min(0, N+1)
if marge_now-offset < 0 or marge_now == INF:
return False, None
remains[num] -= 1
if remains[num] == 0:
marge.update(num, INF)
else:
marge.update(num, marge_now+1)
decided[n] = num
offset += 1
return True, decided[1:]
if __name__ == "__main__":
ok, ans = solve()
if ok:
print("Yes")
print(*ans)
else:
print("No")
``` | output | 1 | 14,892 | 5 | 29,785 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No | instruction | 0 | 14,893 | 5 | 29,786 |
"Correct Solution:
```
import sys
n = int(input())
x = list(map(int, input().split()))
s = sorted([[y-1, i+1] for i, y in enumerate(x)])
cur = 0
cnt = [0 for _ in range(n+1)]
fill_cur = 0
ans = []
residual = []
for i in range(n*n):
if i == s[cur][0] and cnt[s[cur][1]] != s[cur][1]-1:
print("No")
sys.exit()
elif i == s[cur][0]:
ans.append(s[cur][1])
cnt[s[cur][1]] += 1
residual += [s[cur][1]] * (n - s[cur][1])
cur += 1
fill_cur = max(fill_cur, cur)
if cur == n:
break
elif fill_cur < n:
while cnt[s[fill_cur][1]] == s[fill_cur][1]-1:
fill_cur += 1
if fill_cur == n:
if not residual:
print("No")
sys.exit()
ans.append(residual.pop())
break
else:
fill_cur = max(fill_cur, cur)
ans.append(s[fill_cur][1])
cnt[s[fill_cur][1]] += 1
elif not residual:
print("No")
sys.exit()
else:
ans.append(residual.pop())
ans += residual
print("Yes")
print(*ans)
``` | output | 1 | 14,893 | 5 | 29,787 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No | instruction | 0 | 14,894 | 5 | 29,788 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
ans = [-1] * (n ** 2)
for i in range(n):
ans[a[i] - 1] = i + 1
b = sorted([(a[i], i + 1) for i in range(n)], reverse=True)
stack = []
for _, val in b:
for _ in range(val - 1):
stack.append(val)
for i in range(n ** 2):
if ans[i] == -1:
if not stack:
continue
ans[i] = stack.pop()
b = sorted([(a[i], i + 1) for i in range(n)])
stack = []
for _, val in b:
for _ in range(n - val):
stack.append(val)
for i in range(n ** 2)[::-1]:
if ans[i] == -1:
if not stack:
continue
ans[i] = stack.pop()
cnt = [0] * (n + 1)
for i in range(n ** 2):
cnt[ans[i]] += 1
if cnt[ans[i]] == ans[i]:
if a[ans[i] - 1] == i + 1:
continue
else:
print("No")
exit()
print("Yes")
print(*ans)
``` | output | 1 | 14,894 | 5 | 29,789 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No | instruction | 0 | 14,895 | 5 | 29,790 |
"Correct Solution:
```
n = int(input())
x = [int(x) for i, x in enumerate(input().split())]
x = sorted(zip(x, range(1, n+1)))
stack = []
for v, i in x[::-1]:
for _ in range(i-1):
stack.append(i)
cur = 1
ans = []
res = []
cnt = [0]*(n+1)
for i in range(n):
for _ in range(x[i][0]-cur):
if stack:
nxt = stack.pop()
elif res:
nxt = res.pop()
else:
print('No')
exit()
ans.append(nxt)
cnt[nxt] += 1
if cnt[x[i][1]] != x[i][1]-1:
print('No')
exit()
ans.append(x[i][1])
for _ in range(n-x[i][1]):
res.append(x[i][1])
cur = x[i][0]+1
ans += res
print('Yes')
print(*ans)
``` | output | 1 | 14,895 | 5 | 29,791 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No | instruction | 0 | 14,896 | 5 | 29,792 |
"Correct Solution:
```
from heapq import heappop,heappush
n = int(input())
a = list(map(int,input().split()))
dic = dict()
for i,ai in enumerate(a,1):
if(ai-1 in dic):
print('No')
eixt()
dic[ai-1] = i
hq = []
for i,ai in enumerate(a[1:],2):
heappush(hq,(ai-i,i-1,i))
others = []
ans = []
for ind in range(n**2):
if ind in dic:
i = dic[ind]
ans.append(i)
others += [i] * (n-i)
continue
if(hq):
num,rem,i = heappop(hq)
if(num < ind):
print('No')
exit()
elif(rem==1):
ans.append(i)
else:
ans.append(i)
heappush(hq,(num+1,rem-1,i))
else:
if(others):
ans.append(others.pop())
else:
print('No')
exit()
print('Yes')
print(' '.join(map(str,ans)))
``` | output | 1 | 14,896 | 5 | 29,793 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No | instruction | 0 | 14,897 | 5 | 29,794 |
"Correct Solution:
```
from collections import deque
from collections import defaultdict
n = int(input())
x = list(map(int,input().split()))
for i in range(n):
if x[i]-1 < i or x[i]-1 > n*n-n+i:
print("No")
exit()
ans = [-1]*n*n
for i in range(n):
ans[x[i]-1] = i+1
x2 = []
for i in range(n):
x2.append((x[i],i+1))
x2.sort()
yusen = deque([])
ato = deque([])
for i in range(n):
yusen.extend([x2[i][1]]*(x2[i][1]-1))
ato.extend([x2[i][1]]*(n-x2[i][1]))
for i in range(n*n):
if ans[i] == -1:
if yusen:
ko = yusen.popleft()
ans[i] = ko
else:
ko = ato.popleft()
ans[i] = ko
d = defaultdict(int)
for i in range(n*n):
d[ans[i]] += 1
if d[ans[i]] == ans[i]:
if i+1 != x[ans[i]-1]:
print("No")
exit()
print("Yes")
print(*ans)
``` | output | 1 | 14,897 | 5 | 29,795 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No | instruction | 0 | 14,898 | 5 | 29,796 |
"Correct Solution:
```
N = int(input())
ans = [-1] * (N ** 2)
X = [int(x)-1 for x in input().split()]
for i, x in enumerate(X):
ans[x] = i+1
left, right = [], []
for i in range(N):
l_cnt, r_cnt = i, N - (i+1)
left.extend([(X[i], i+1)] * l_cnt)
right.extend([(X[i], i+1)] * r_cnt)
l, r = 0, N ** 2 - 1
left.sort()
right.sort(reverse=True)
for _, x in left:
while ans[l] != -1:
l += 1
ans[l] = x
for _, x in right:
while ans[r] != -1:
r -= 1
ans[r] = x
counter = [[] for _ in range(N)]
for i, a in enumerate(ans):
counter[a-1].append(i)
if all(counter[i].index(x) == i for i, x in zip(range(N), X)):
print("Yes")
print(*ans)
else:
print("No")
``` | output | 1 | 14,898 | 5 | 29,797 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No | instruction | 0 | 14,899 | 5 | 29,798 |
"Correct Solution:
```
def solve():
n=int(input())
x=list(map(int,input().split()))
list1=[]
def ap1(num):
list1.append(num)
for i in range(n):
ap1([x[i],i+1])
str1= lambda val: val[0]
list1.sort(key=str1)
numa=[]
numb=[]
for i in range(n):
num3=list1[i][1]
numa+=[num3]*(num3-1)
numb+=[num3]*(n-num3)
count1=0
count2=0
count3=0
ans=[]
ansnum=0
def countnum(num):
return ans.count(num)
def apans(num):
ans.append(num)
for i in range(n*n):
yn=0
if count1!=n:
if i==list1[count1][0]-1:
if countnum(list1[count1][1])!=list1[count1][1]-1:
ansnum=1
break
apans(list1[count1][1])
count1+=1
yn=1
if yn==0:
if count2!=len(numa):
apans(numa[count2])
count2+=1
elif count3!=len(numb):
apans(numb[count3])
count3+=1
else:
if i!=n*n-1:
ansnum=1
break
if ansnum==1:
print("No")
else:
print("Yes")
print(*ans)
solve()
``` | output | 1 | 14,899 | 5 | 29,799 |
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 sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No
Submitted Solution:
```
import collections
n = int(input())
x = list(map(int, input().split()))
x = list(enumerate(x, 1))
x.sort(key = lambda x: x[1])
li = []
dic = {j: i for i, j in x}
for i, j in x:
li += [i] * (i - 1)
for i, j in x:
li += [i] * (n - i)
li = collections.deque(li)
ans = []
cnt = [0 for i in range(n + 1)]
for i in range(1, n ** 2 + 1):
if i in dic:
m = dic[i]
if cnt[m] != m - 1:
print("No")
exit()
else:
m = li.popleft()
cnt[m] += 1
ans.append(m)
print("Yes")
print(*ans)
``` | instruction | 0 | 14,900 | 5 | 29,800 |
Yes | output | 1 | 14,900 | 5 | 29,801 |
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 sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No
Submitted Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
b = [(a[i], i) for i in range(N)]
b.sort()
res = [0] * pow(N, 2)
for i in range(N): res[a[i] - 1] = i + 1
#print(res, b)
for k in range(N):
i = b[k][1]
x = i
if i == 0: continue
for j in range(a[i] - 1):
if res[j]: continue
res[j] = i + 1
x -= 1
if x == 0: break
#print(res, i, a[i])
if x:
print("No")
exit(0)
#print(res)
#print(res)
for i in range(N):
x = N - i - 1
for j in range(a[i], N ** 2):
if res[j]: continue
res[j] = i + 1
x -= 1
if x == 0: break
#print(res)
if x:
print("No")
exit(0)
print("Yes")
print(*res)
``` | instruction | 0 | 14,901 | 5 | 29,802 |
Yes | output | 1 | 14,901 | 5 | 29,803 |
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 sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No
Submitted Solution:
```
N=int(input())
x=list(map(int,input().split()))
ans=[0]*(N**2)
x=[(x[i]-1,i+1) for i in range(N)]
x.sort()
for i in range(N):
p,v=x[i]
ans[p]=v
pos=0
for i in range(N):
val,count=x[i]
count-=1
while count:
while ans[pos]:
pos+=1
if pos>=val:
print("No")
exit()
else:
ans[pos]=x[i][1]
count-=1
pos=N**2-1
for i in range(N-1,-1,-1):
val,count=x[i]
count-=1
count=N-1-count
while count:
while ans[pos]:
pos-=1
if val>=pos:
print("No")
exit()
else:
ans[pos]=x[i][1]
count-=1
print("Yes")
print(*ans)
``` | instruction | 0 | 14,902 | 5 | 29,804 |
Yes | output | 1 | 14,902 | 5 | 29,805 |
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 sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No
Submitted Solution:
```
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)
N = int(input())
X = sorted((x,i) for i,x in enumerate((int(x) for x in input().split()),1))
arr = []
for x,i in X:
arr += [i] * (i-1)
for x,i in X:
arr += [i] * (N-i)
x_to_i = dict(X)
arr = arr[::-1]
answer = []
counter = [0] * (N+1)
bl = True
for x in range(1,N*N+1):
if x in x_to_i:
i = x_to_i[x]
counter[i] += 1
bl &= (counter[i] == i)
else:
i = arr.pop()
counter[i] += 1
answer.append(i)
if bl:
print('Yes')
print(*answer)
else:
print('No')
``` | instruction | 0 | 14,903 | 5 | 29,806 |
Yes | output | 1 | 14,903 | 5 | 29,807 |
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 sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No
Submitted Solution:
```
n=int(input())
x=[]
xx=list(map(int,input().split()))
for i in range(n):x.append([xx[i],i+1])
x.sort()
ans=[0]*n*n
c=[n]*n
l=[0]*(n*n+1)
r=[0]*(n*n+1)
for t,i in x:r[t]=n-i
for i in range(n*n):
if r[i]!=0:
r[i+1]+=r[i]-1
if r[n]:exit(print("No"))
for t,i in x[::-1]:l[t-1]=i-1
for i in range(n*n,0,-1):
if l[i]!=0:
l[i-1]+=l[i]-1
if l[0]:exit(print("No"))
x+=[[10**10,10**10]]
ind=0
d=[]
for i in range(n*n):
if i==x[ind][0]:
d+=[x[ind][1]]*(n-x[ind][1])
ind+=1
if d:ans[i]=d.pop()
x=x[:-1][::-1]+[[-10,-10]]
ind=0
d=[]
for i in range(n*n,-1,-1):
if i==x[ind][0]:
ans[i-1]=x[ind][1]
d+=[x[ind][1]]*x[ind][1]
ind+=1
if d:ans[i-1]=d.pop()
print("Yes")
print(*ans)
``` | instruction | 0 | 14,904 | 5 | 29,808 |
No | output | 1 | 14,904 | 5 | 29,809 |
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 sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No
Submitted Solution:
```
import os
import sys
from collections import deque, defaultdict
if os.getenv("LOCAL"):
sys.stdin = open("_in.txt", "r")
sys.setrecursionlimit(10 ** 9)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7
# MOD = 998244353
N = int(sys.stdin.buffer.readline())
X = list(map(int, sys.stdin.buffer.readline().split()))
ans = [None] * (N ** 2 + 1)
# 左にあるものから使う
P = list(sorted([(pos, i) for i, pos in enumerate(X, 1)]))
que = deque()
for p, i in P:
ans[p] = i
for _ in range(i - 1):
que.append(i)
for p in range(1, N ** 2 + 1):
if not que:
break
if ans[p] is not None:
i = ans[p]
for _ in range(N - i):
que.append(i)
else:
ans[p] = que.popleft()
def is_ok(ans, que):
if que:
return False
for a in ans[1:]:
if a is None:
return False
counts = defaultdict(int)
C = [0]
for a in ans[1:]:
counts[a] += 1
C.append(counts[a])
for i, x in enumerate(X, 1):
if C[x] != i:
return False
return True
if is_ok(ans, que):
print('Yes')
print(*ans[1:])
else:
print('No')
``` | instruction | 0 | 14,905 | 5 | 29,810 |
No | output | 1 | 14,905 | 5 | 29,811 |
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 sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No
Submitted Solution:
```
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
def readln(ch):
_res = list(map(int,str(input()).split(ch)))
return _res
def construct(x):
a = sorted([(x[i] - 1) * 1000 + i for i in range(0,n)])
res = [0 for i in range(0,n) for j in range(0,n)]
r = 0
for i in range(0,n):
res[a[i] // 1000] = i + 1
while res[r] > 0 : r = r + 1
for i in range(0,n):
index = a[i] % 1000
x = a[i] // 1000
for j in range(0,index):
if r > x:
return [True]
res[r] = index + 1
while res[r] > 0: r = r + 1
for i in range(0,n):
for j in range(0,n - i - 1):
res[r] = i + 1
while r < n * n and res[r] > 0 :
r = r + 1
return [False,res]
n = int(input())
x = readln(' ')
res = construct(x)
if res[0]:
print('No')
else:
print('Yes')
print(' '.join(list(map(str,res[1]))))
``` | instruction | 0 | 14,906 | 5 | 29,812 |
No | output | 1 | 14,906 | 5 | 29,813 |
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 sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.
* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.
Constraints
* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
Output
If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.
Examples
Input
3
1 5 9
Output
Yes
1 1 1 2 2 2 3 3 3
Input
2
4 1
Output
No
Submitted Solution:
```
N = int(input())
ans = [-1] * (N ** 2)
X = [int(x)-1 for x in input().split()]
for i, x in enumerate(X):
ans[x] = i+1
left, right = 0, N ** 2 - 1
for i in range(N):
l_cnt, r_cnt = i, N - (i+1)
for _ in range(l_cnt):
while ans[left] != -1:
left += 1
ans[left] = i+1
for _ in range(r_cnt):
while ans[right] != -1:
right -= 1
ans[right] = i+1
counter = [[] for _ in range(N)]
for i, a in enumerate(ans):
counter[a-1].append(i)
if all(counter[i].index(x) == i for i, x in zip(range(N), X)):
print("Yes")
print(*ans)
else:
print("No")
assert(all(a != -1 for a in ans))
assert(all(len(row) == N for row in counter))
``` | instruction | 0 | 14,907 | 5 | 29,814 |
No | output | 1 | 14,907 | 5 | 29,815 |
Provide a correct Python 3 solution for this coding contest problem.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8 | instruction | 0 | 15,046 | 5 | 30,092 |
"Correct Solution:
```
if __name__ == '__main__':
input()
A = set(map(int,input().split()))
input()
B = set(map(int,input().split()))
C = sorted(A^B)
for i in C:
print(i)
``` | output | 1 | 15,046 | 5 | 30,093 |
Provide a correct Python 3 solution for this coding contest problem.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8 | instruction | 0 | 15,047 | 5 | 30,094 |
"Correct Solution:
```
input()
A = set(int(x) for x in input().split())
input()
B = set(int(x) for x in input().split())
for i in sorted((A | B) - (A & B)):
print(i)
``` | output | 1 | 15,047 | 5 | 30,095 |
Provide a correct Python 3 solution for this coding contest problem.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8 | instruction | 0 | 15,048 | 5 | 30,096 |
"Correct Solution:
```
input()
A = set([int(x) for x in input().split() ])
input()
B = set([int(x) for x in input().split() ])
for i in sorted(A^B):
print(i)
``` | output | 1 | 15,048 | 5 | 30,097 |
Provide a correct Python 3 solution for this coding contest problem.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8 | instruction | 0 | 15,049 | 5 | 30,098 |
"Correct Solution:
```
input()
s1 = set(map(int, input().split()))
input()
s2 = set(map(int, input().split()))
s = sorted(list(s1.symmetric_difference(s2)))
if len(s) != 0:
print('\n'.join(map(str, s)))
``` | output | 1 | 15,049 | 5 | 30,099 |
Provide a correct Python 3 solution for this coding contest problem.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8 | instruction | 0 | 15,050 | 5 | 30,100 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
"""
Set Operation - Set Symmetric Difference
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP2_9_D&lang=jp
"""
_ = input()
A = set([int(a) for a in input().split()])
_ = input()
B = set([int(b) for b in input().split()])
C = sorted(d for d in (A ^ B))
if C:
print(*C, sep='\n')
``` | output | 1 | 15,050 | 5 | 30,101 |
Provide a correct Python 3 solution for this coding contest problem.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8 | instruction | 0 | 15,051 | 5 | 30,102 |
"Correct Solution:
```
n = int(input())
alist = list(map(int, input().split()))
m = int(input())
blist = list(map(int, input().split()))
anslist = set(alist) ^ set(blist)
anslist = list(anslist)
anslist.sort()
for ans in anslist:
print(ans)
``` | output | 1 | 15,051 | 5 | 30,103 |
Provide a correct Python 3 solution for this coding contest problem.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8 | instruction | 0 | 15,052 | 5 | 30,104 |
"Correct Solution:
```
n = int(input())
a = set(map(int, input().split()))
m = int(input())
b = set(map(int, input().split()))
for n in sorted(a ^ b): print(n)
``` | output | 1 | 15,052 | 5 | 30,105 |
Provide a correct Python 3 solution for this coding contest problem.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8 | instruction | 0 | 15,053 | 5 | 30,106 |
"Correct Solution:
```
n=input()
a=set(map(int, input().split()))
n=input()
b=set(map(int, input().split()))
c={print(x) for x in sorted(set(a^b))}
``` | output | 1 | 15,053 | 5 | 30,107 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8
Submitted Solution:
```
n = int(input())
A = set(list(map(int, input().split())))
m = int(input())
B = set(list(map(int, input().split())))
answer = A.symmetric_difference(B)
[print(i) for i in sorted(answer)]
``` | instruction | 0 | 15,054 | 5 | 30,108 |
Yes | output | 1 | 15,054 | 5 | 30,109 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8
Submitted Solution:
```
if __name__ == "__main__":
n = int(input())
a = set(map(lambda x: int(x), input().split()))
m = int(input())
b = set(map(lambda x: int(x), input().split()))
for elem in sorted(a.union(b) - a.intersection(b)):
print(elem)
``` | instruction | 0 | 15,055 | 5 | 30,110 |
Yes | output | 1 | 15,055 | 5 | 30,111 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8
Submitted Solution:
```
n=int(input())
A=list(map(int,input().split()))
m=int(input())
B=list(map(int,input().split()))
C=list(set(A)^set(B))
C.sort()
if C!=[]:
print('\n'.join(map(str,C)))
``` | instruction | 0 | 15,056 | 5 | 30,112 |
Yes | output | 1 | 15,056 | 5 | 30,113 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the symmetric difference of two sets $A = \\{a_0, a_1, ..., a_{n-1}\\}$ and $B = \\{b_0, b_1, ..., b_{m-1}\\}$.
Constraints
* $1 \leq n, m \leq 200,000$
* $0 \leq a_0 < a_1 < ... < a_{n-1} \leq 10^9$
* $0 \leq b_0 < b_1 < ... < b_{m-1} \leq 10^9$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ... \; a_{n-1}$
$m$
$b_0 \; b_1 \; ... \; b_{m-1}$
Elements in $A$ and $B$ are given in ascending order. There are no duplicate elements in each set.
Output
Print elements in the symmetric difference in ascending order. Print an element in a line.
Example
Input
7
1 2 3 4 5 6 7
4
2 4 6 8
Output
1
3
5
7
8
Submitted Solution:
```
n = int(input())
a = set(list(map(int, input().split())))
m = int(input())
b = set(list(map(int, input().split())))
for i in sorted(a^b):
print(i)
``` | instruction | 0 | 15,057 | 5 | 30,114 |
Yes | output | 1 | 15,057 | 5 | 30,115 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gottfried learned about binary number representation. He then came up with this task and presented it to you.
You are given a collection of n non-negative integers a_1, …, a_n. You are allowed to perform the following operation: choose two distinct indices 1 ≤ i, j ≤ n. If before the operation a_i = x, a_j = y, then after the operation a_i = x~AND~y, a_j = x~OR~y, where AND and OR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).
After all operations are done, compute ∑_{i=1}^n a_i^2 — the sum of squares of all a_i. What is the largest sum of squares you can achieve?
Input
The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line contains n integers a_1, …, a_n (0 ≤ a_i < 2^{20}).
Output
Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.
Examples
Input
1
123
Output
15129
Input
3
1 3 5
Output
51
Input
2
349525 699050
Output
1099509530625
Note
In the first sample no operation can be made, thus the answer is 123^2.
In the second sample we can obtain the collection 1, 1, 7, and 1^2 + 1^2 + 7^2 = 51.
If x and y are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x~AND~y is set to 1 if and only if both corresponding bits of x and y are set to 1. Similarly, each bit of x~OR~y is set to 1 if and only if at least one of the corresponding bits of x and y are set to 1. For example, x = 3 and y = 5 are represented as 011_2 and 101_2 (highest bit first). Then, x~AND~y = 001_2 = 1, and x~OR~y = 111_2 = 7.
Submitted Solution:
```
n=int(input())
arr=list(map(int,input().split()))
binary=[0]*20
for val in arr:
temp=0
while(val):
if(val & 1):
binary[temp]+=1
val>>=1
temp+=1
ans=0
for i in range(n):
temp=0
for place in range(20):
if(binary[place]):
temp+=(1<<place)
binary[place]-=1
ans+=(temp**2)
print(ans)
``` | instruction | 0 | 15,238 | 5 | 30,476 |
Yes | output | 1 | 15,238 | 5 | 30,477 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gottfried learned about binary number representation. He then came up with this task and presented it to you.
You are given a collection of n non-negative integers a_1, …, a_n. You are allowed to perform the following operation: choose two distinct indices 1 ≤ i, j ≤ n. If before the operation a_i = x, a_j = y, then after the operation a_i = x~AND~y, a_j = x~OR~y, where AND and OR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).
After all operations are done, compute ∑_{i=1}^n a_i^2 — the sum of squares of all a_i. What is the largest sum of squares you can achieve?
Input
The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line contains n integers a_1, …, a_n (0 ≤ a_i < 2^{20}).
Output
Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.
Examples
Input
1
123
Output
15129
Input
3
1 3 5
Output
51
Input
2
349525 699050
Output
1099509530625
Note
In the first sample no operation can be made, thus the answer is 123^2.
In the second sample we can obtain the collection 1, 1, 7, and 1^2 + 1^2 + 7^2 = 51.
If x and y are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x~AND~y is set to 1 if and only if both corresponding bits of x and y are set to 1. Similarly, each bit of x~OR~y is set to 1 if and only if at least one of the corresponding bits of x and y are set to 1. For example, x = 3 and y = 5 are represented as 011_2 and 101_2 (highest bit first). Then, x~AND~y = 001_2 = 1, and x~OR~y = 111_2 = 7.
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
deg_count = []
for i in range(n):
deg = 0
while a[i] > 0:
# print("a[i]", a[i])
if deg > len(deg_count) - 1:
deg_count.append(0)
if a[i] & 1:
deg_count[deg] += 1
a[i] >>= 1
deg += 1
# print("deg", deg)
# print(*deg_count, sep=" ")
ans = 0
for i in range(n):
num = 0
for deg in range(len(deg_count)):
if deg_count[deg] > 0:
num += 1 << deg
deg_count[deg] -= 1
ans += num*num
print(ans)
``` | instruction | 0 | 15,239 | 5 | 30,478 |
Yes | output | 1 | 15,239 | 5 | 30,479 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gottfried learned about binary number representation. He then came up with this task and presented it to you.
You are given a collection of n non-negative integers a_1, …, a_n. You are allowed to perform the following operation: choose two distinct indices 1 ≤ i, j ≤ n. If before the operation a_i = x, a_j = y, then after the operation a_i = x~AND~y, a_j = x~OR~y, where AND and OR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).
After all operations are done, compute ∑_{i=1}^n a_i^2 — the sum of squares of all a_i. What is the largest sum of squares you can achieve?
Input
The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line contains n integers a_1, …, a_n (0 ≤ a_i < 2^{20}).
Output
Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.
Examples
Input
1
123
Output
15129
Input
3
1 3 5
Output
51
Input
2
349525 699050
Output
1099509530625
Note
In the first sample no operation can be made, thus the answer is 123^2.
In the second sample we can obtain the collection 1, 1, 7, and 1^2 + 1^2 + 7^2 = 51.
If x and y are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x~AND~y is set to 1 if and only if both corresponding bits of x and y are set to 1. Similarly, each bit of x~OR~y is set to 1 if and only if at least one of the corresponding bits of x and y are set to 1. For example, x = 3 and y = 5 are represented as 011_2 and 101_2 (highest bit first). Then, x~AND~y = 001_2 = 1, and x~OR~y = 111_2 = 7.
Submitted Solution:
```
def prog():
n = int(input())
nums = list(map(int,input().split()))
amounts = [0]*20
for num in nums:
num = bin(num)[:1:-1]
for i in range(len(num)):
amounts[i] += "1" == num[i]
totals = []
while True:
left = False
for amount in amounts:
if amount:
left = True
break
if not left:
break
curr = 0
for i in range(20):
if amounts[i]:
amounts[i] -= 1
curr += 1 << i
totals.append(curr)
ans = 0
for total in totals:
ans += total**2
print(ans)
prog()
``` | instruction | 0 | 15,240 | 5 | 30,480 |
Yes | output | 1 | 15,240 | 5 | 30,481 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gottfried learned about binary number representation. He then came up with this task and presented it to you.
You are given a collection of n non-negative integers a_1, …, a_n. You are allowed to perform the following operation: choose two distinct indices 1 ≤ i, j ≤ n. If before the operation a_i = x, a_j = y, then after the operation a_i = x~AND~y, a_j = x~OR~y, where AND and OR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).
After all operations are done, compute ∑_{i=1}^n a_i^2 — the sum of squares of all a_i. What is the largest sum of squares you can achieve?
Input
The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line contains n integers a_1, …, a_n (0 ≤ a_i < 2^{20}).
Output
Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.
Examples
Input
1
123
Output
15129
Input
3
1 3 5
Output
51
Input
2
349525 699050
Output
1099509530625
Note
In the first sample no operation can be made, thus the answer is 123^2.
In the second sample we can obtain the collection 1, 1, 7, and 1^2 + 1^2 + 7^2 = 51.
If x and y are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x~AND~y is set to 1 if and only if both corresponding bits of x and y are set to 1. Similarly, each bit of x~OR~y is set to 1 if and only if at least one of the corresponding bits of x and y are set to 1. For example, x = 3 and y = 5 are represented as 011_2 and 101_2 (highest bit first). Then, x~AND~y = 001_2 = 1, and x~OR~y = 111_2 = 7.
Submitted Solution:
```
import sys, math,os
from io import BytesIO, IOBase
# data = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# from bisect import bisect_left as bl, bisect_right as br, insort
# from heapq import heapify, heappush, heappop
from collections import defaultdict as dd, deque, Counter
# from itertools import permutations,combinations
# from decimal import Decimal
def data(): return sys.stdin.buffer.readline().strip()
def mdata(): return list(map(int, data().split()))
def outl(var): sys.stdout.write(' '.join(map(str, var)) + '\n')
def out(var): sys.stdout.write(str(var) + '\n')
#sys.setrecursionlimit(100000 + 1)
#INF = float('inf')
mod = 998244353
n=int(data())
a=mdata()
d=[[0]*20 for i in range(n+1)]
a.sort()
for i in range(n-1,-1,-1):
d[i]=d[i+1][:]
b=bin(a[i])[2:][::-1]
for j in range(len(b)):
if b[j]=='0':
d[i][j]+=1
ans=0
d1=[0]*20
for i in range(n):
b = list(bin(a[i])[2:][::-1])
for j in range(len(b)):
if b[j]=='1' and d[i][j]+d1[j]>0:
b[j]='0'
d1[j]-=1
else:
if d[i][j]+d1[j]<=0:
b[j]='1'
ans+=int(''.join(b[::-1]),2)**2
out(ans)
``` | instruction | 0 | 15,241 | 5 | 30,482 |
Yes | output | 1 | 15,241 | 5 | 30,483 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gottfried learned about binary number representation. He then came up with this task and presented it to you.
You are given a collection of n non-negative integers a_1, …, a_n. You are allowed to perform the following operation: choose two distinct indices 1 ≤ i, j ≤ n. If before the operation a_i = x, a_j = y, then after the operation a_i = x~AND~y, a_j = x~OR~y, where AND and OR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).
After all operations are done, compute ∑_{i=1}^n a_i^2 — the sum of squares of all a_i. What is the largest sum of squares you can achieve?
Input
The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line contains n integers a_1, …, a_n (0 ≤ a_i < 2^{20}).
Output
Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.
Examples
Input
1
123
Output
15129
Input
3
1 3 5
Output
51
Input
2
349525 699050
Output
1099509530625
Note
In the first sample no operation can be made, thus the answer is 123^2.
In the second sample we can obtain the collection 1, 1, 7, and 1^2 + 1^2 + 7^2 = 51.
If x and y are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x~AND~y is set to 1 if and only if both corresponding bits of x and y are set to 1. Similarly, each bit of x~OR~y is set to 1 if and only if at least one of the corresponding bits of x and y are set to 1. For example, x = 3 and y = 5 are represented as 011_2 and 101_2 (highest bit first). Then, x~AND~y = 001_2 = 1, and x~OR~y = 111_2 = 7.
Submitted Solution:
```
import sys
from collections import defaultdict as dd
from collections import deque
from fractions import Fraction as f
from itertools import permutations
def eprint(*args):
print(*args, file=sys.stderr)
zz=1
from math import *
import copy
#sys.setrecursionlimit(10**6)
if zz:
input=sys.stdin.readline
else:
sys.stdin=open('input.txt', 'r')
sys.stdout=open('all.txt','w')
def li():
return [int(x) for x in input().split()]
def fi():
return int(input())
def si():
return list(input().rstrip())
def mi():
return map(int,input().split())
def gh():
sys.stdout.flush()
def bo(i):
return ord(i)-ord('a')
from copy import *
from bisect import *
def lol(p):
h=bin(p)[2:]
h="0"*(60-len(h))+h
print(h)
n=fi()
a=li()
ans=0
c=[0 for i in range(31)]
for i in range(n):
for j in range(30):
if a[i]&(1<<j):
c[j]+=1
for i in range(n):
x=0
for j in range(30):
if c[j]>0:
c[j]-=1
x|=(1<<j)
ans+=x**2
print(ans)
``` | instruction | 0 | 15,242 | 5 | 30,484 |
No | output | 1 | 15,242 | 5 | 30,485 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gottfried learned about binary number representation. He then came up with this task and presented it to you.
You are given a collection of n non-negative integers a_1, …, a_n. You are allowed to perform the following operation: choose two distinct indices 1 ≤ i, j ≤ n. If before the operation a_i = x, a_j = y, then after the operation a_i = x~AND~y, a_j = x~OR~y, where AND and OR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).
After all operations are done, compute ∑_{i=1}^n a_i^2 — the sum of squares of all a_i. What is the largest sum of squares you can achieve?
Input
The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line contains n integers a_1, …, a_n (0 ≤ a_i < 2^{20}).
Output
Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.
Examples
Input
1
123
Output
15129
Input
3
1 3 5
Output
51
Input
2
349525 699050
Output
1099509530625
Note
In the first sample no operation can be made, thus the answer is 123^2.
In the second sample we can obtain the collection 1, 1, 7, and 1^2 + 1^2 + 7^2 = 51.
If x and y are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x~AND~y is set to 1 if and only if both corresponding bits of x and y are set to 1. Similarly, each bit of x~OR~y is set to 1 if and only if at least one of the corresponding bits of x and y are set to 1. For example, x = 3 and y = 5 are represented as 011_2 and 101_2 (highest bit first). Then, x~AND~y = 001_2 = 1, and x~OR~y = 111_2 = 7.
Submitted Solution:
```
import sys
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))
n,=I()
l=sorted(I())
an=0
for i in range(n-1):
x=l[i]
l[i]=l[i]&l[i+1]
an+=l[i]*l[i]
l[i+1]|=x
an+=l[n-1]*l[n-1]
print(an)
``` | instruction | 0 | 15,243 | 5 | 30,486 |
No | output | 1 | 15,243 | 5 | 30,487 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gottfried learned about binary number representation. He then came up with this task and presented it to you.
You are given a collection of n non-negative integers a_1, …, a_n. You are allowed to perform the following operation: choose two distinct indices 1 ≤ i, j ≤ n. If before the operation a_i = x, a_j = y, then after the operation a_i = x~AND~y, a_j = x~OR~y, where AND and OR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).
After all operations are done, compute ∑_{i=1}^n a_i^2 — the sum of squares of all a_i. What is the largest sum of squares you can achieve?
Input
The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line contains n integers a_1, …, a_n (0 ≤ a_i < 2^{20}).
Output
Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.
Examples
Input
1
123
Output
15129
Input
3
1 3 5
Output
51
Input
2
349525 699050
Output
1099509530625
Note
In the first sample no operation can be made, thus the answer is 123^2.
In the second sample we can obtain the collection 1, 1, 7, and 1^2 + 1^2 + 7^2 = 51.
If x and y are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x~AND~y is set to 1 if and only if both corresponding bits of x and y are set to 1. Similarly, each bit of x~OR~y is set to 1 if and only if at least one of the corresponding bits of x and y are set to 1. For example, x = 3 and y = 5 are represented as 011_2 and 101_2 (highest bit first). Then, x~AND~y = 001_2 = 1, and x~OR~y = 111_2 = 7.
Submitted Solution:
```
def solve(n, l):
l = sorted(l)[::-1]
ans = 0
i = 0
while i < n:
p_org = l[i-1]*l[i-1] + l[i]*l[i]
g = l[i-1]&l[i]
h = l[i-1]|l[i]
p_new = g*g + h*h
if p_new > p_org:
l[i-1] = h
l[i] = g
l = sorted(l)[::-1]
i += 1
for i in range(n):
ans += l[i]*l[i]
return ans
n = int(input())
l = list(map(int, input().split()))
print(solve(n, l))
``` | instruction | 0 | 15,244 | 5 | 30,488 |
No | output | 1 | 15,244 | 5 | 30,489 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gottfried learned about binary number representation. He then came up with this task and presented it to you.
You are given a collection of n non-negative integers a_1, …, a_n. You are allowed to perform the following operation: choose two distinct indices 1 ≤ i, j ≤ n. If before the operation a_i = x, a_j = y, then after the operation a_i = x~AND~y, a_j = x~OR~y, where AND and OR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).
After all operations are done, compute ∑_{i=1}^n a_i^2 — the sum of squares of all a_i. What is the largest sum of squares you can achieve?
Input
The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line contains n integers a_1, …, a_n (0 ≤ a_i < 2^{20}).
Output
Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.
Examples
Input
1
123
Output
15129
Input
3
1 3 5
Output
51
Input
2
349525 699050
Output
1099509530625
Note
In the first sample no operation can be made, thus the answer is 123^2.
In the second sample we can obtain the collection 1, 1, 7, and 1^2 + 1^2 + 7^2 = 51.
If x and y are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x~AND~y is set to 1 if and only if both corresponding bits of x and y are set to 1. Similarly, each bit of x~OR~y is set to 1 if and only if at least one of the corresponding bits of x and y are set to 1. For example, x = 3 and y = 5 are represented as 011_2 and 101_2 (highest bit first). Then, x~AND~y = 001_2 = 1, and x~OR~y = 111_2 = 7.
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
a.sort(reverse=True)
s = 0
l = []
if n == 1:
print(a[0]*a[0])
else:
for i in range(1,len(a),2):
l.append(a[i] & a[i - 1])
l.append(a[i] | a[i-1])
for i in range(len(l)):
l[i] = l[i]*l[i]
if n%2 != 0:
print(sum(l)+1)
else:
print(sum(l))
``` | instruction | 0 | 15,245 | 5 | 30,490 |
No | output | 1 | 15,245 | 5 | 30,491 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space.
Output
Output "YES" or "NO".
Examples
Input
2 3
Output
YES
Input
3 2
Output
NO
Input
33 16
Output
YES
Input
26 5
Output
NO | instruction | 0 | 15,305 | 5 | 30,610 |
Tags: *special, number theory
Correct Solution:
```
n,m=map(int,input().split());a=[]
while n:a+=[n%m];n//=m
print("YNEOS"[len(set(a))<len(a)::2])
``` | output | 1 | 15,305 | 5 | 30,611 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space.
Output
Output "YES" or "NO".
Examples
Input
2 3
Output
YES
Input
3 2
Output
NO
Input
33 16
Output
YES
Input
26 5
Output
NO | instruction | 0 | 15,306 | 5 | 30,612 |
Tags: *special, number theory
Correct Solution:
```
n, m = map(int, input().split())
l = []
while n > 0:
l.append(n % m)
n = n // m
# print(l)
print("YES" if len(l) == len(set(l)) else "NO")
``` | output | 1 | 15,306 | 5 | 30,613 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space.
Output
Output "YES" or "NO".
Examples
Input
2 3
Output
YES
Input
3 2
Output
NO
Input
33 16
Output
YES
Input
26 5
Output
NO | instruction | 0 | 15,308 | 5 | 30,616 |
Tags: *special, number theory
Correct Solution:
```
n, m = map(int, input().split())
tmp = []
while n:
tmp.append(n % m)
n //= m
if len(tmp) == len(set(tmp)):
print('YES')
else:
print('NO')
``` | output | 1 | 15,308 | 5 | 30,617 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space.
Output
Output "YES" or "NO".
Examples
Input
2 3
Output
YES
Input
3 2
Output
NO
Input
33 16
Output
YES
Input
26 5
Output
NO | instruction | 0 | 15,309 | 5 | 30,618 |
Tags: *special, number theory
Correct Solution:
```
n,m = map(int,input().split());a = []
while n: a.append(n % m);n //= m
print("YES") if(len(set(a)) == len(a)) else print("NO")
``` | output | 1 | 15,309 | 5 | 30,619 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space.
Output
Output "YES" or "NO".
Examples
Input
2 3
Output
YES
Input
3 2
Output
NO
Input
33 16
Output
YES
Input
26 5
Output
NO | instruction | 0 | 15,311 | 5 | 30,622 |
Tags: *special, number theory
Correct Solution:
```
import sys
import math
from math import factorial, inf, gcd
from heapq import *
from functools import *
from itertools import *
from collections import *
from typing import *
from bisect import *
import random
sys.setrecursionlimit(10**5)
def rarray():
return [int(i) for i in input().split()]
t = 1
# t = int(input())
for ii in range(t):
n, m = rarray()
h = set()
f = True
while n > 0:
t = n % m
if t in h:
f = False
break
h.add(t)
n //= m
print('YES' if f else 'NO')
``` | output | 1 | 15,311 | 5 | 30,623 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space.
Output
Output "YES" or "NO".
Examples
Input
2 3
Output
YES
Input
3 2
Output
NO
Input
33 16
Output
YES
Input
26 5
Output
NO
Submitted Solution:
```
def s(a, b):
r = []
while b > 0:
r += [b % a]
b //= a
if len(r) == len(set(r)):
print('YES')
else:
print('NO')
a, b = map(int, input().split())
s(b, a)
``` | instruction | 0 | 15,313 | 5 | 30,626 |
Yes | output | 1 | 15,313 | 5 | 30,627 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space.
Output
Output "YES" or "NO".
Examples
Input
2 3
Output
YES
Input
3 2
Output
NO
Input
33 16
Output
YES
Input
26 5
Output
NO
Submitted Solution:
```
n, k = map(int, input().split())
s = set()
ch = 1
flag = False
while n:
d = n%k
if d in s:
flag = True
break
s.add(d)
n = n//k
if flag:
print("NO")
else:
print("YES")
``` | instruction | 0 | 15,315 | 5 | 30,630 |
Yes | output | 1 | 15,315 | 5 | 30,631 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space.
Output
Output "YES" or "NO".
Examples
Input
2 3
Output
YES
Input
3 2
Output
NO
Input
33 16
Output
YES
Input
26 5
Output
NO
Submitted Solution:
```
n, m = map(int, input().split())
a = []
while n > 0:
a.append(n % m)
n //= m
print("YES" if len(set(a)) == len(a) else "NO")
``` | instruction | 0 | 15,316 | 5 | 30,632 |
Yes | output | 1 | 15,316 | 5 | 30,633 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The input contains two integers N, M (1 ≤ N ≤ 1024, 2 ≤ M ≤ 16), separated by a single space.
Output
Output "YES" or "NO".
Examples
Input
2 3
Output
YES
Input
3 2
Output
NO
Input
33 16
Output
YES
Input
26 5
Output
NO
Submitted Solution:
```
n,m=input().split()
x,y=0,0
for i in n:
x+=int(i)
for j in m:
y+=int(j)
if(x <= y):
print("YES")
else:
print("NO")
``` | instruction | 0 | 15,317 | 5 | 30,634 |
No | output | 1 | 15,317 | 5 | 30,635 |
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