message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0 | instruction | 0 | 83,996 | 16 | 167,992 |
"Correct Solution:
```
n=int(input())
num=[0]+[int(i) for i in input().split()]
ans=[]
for i in range(n,0,-1):
cnt,j=0,2
while i*j<=n:
cnt+=num[i*j]
j+=1
if cnt%2==num[i]:
num[i]=0
else:
num[i]=1
ans.append(i)
print(len(ans))
print(*ans)
``` | output | 1 | 83,996 | 16 | 167,993 |
Provide a correct Python 3 solution for this coding contest problem.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0 | instruction | 0 | 83,997 | 16 | 167,994 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
a =[0]+ list(map(int, input().split()))
for i in range(N,0,-1):
a[i] =sum(a[i::i]) %2
print(sum(a))
del a[0]
for i,v in enumerate(a):
if v==1:
print(i+1,end=" ")
``` | output | 1 | 83,997 | 16 | 167,995 |
Provide a correct Python 3 solution for this coding contest problem.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0 | instruction | 0 | 83,998 | 16 | 167,996 |
"Correct Solution:
```
n = int(input())
a = [int(x) for x in input().split()]
ans = [0]*n
for i in range(n-1, -1, -1):
ans[i] = sum(ans[i+i+1:n:i+1]) % 2 != a[i]
print(sum(ans))
for i in range(n):
if ans[i] == 1:
print(i+1)
``` | output | 1 | 83,998 | 16 | 167,997 |
Provide a correct Python 3 solution for this coding contest problem.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0 | instruction | 0 | 83,999 | 16 | 167,998 |
"Correct Solution:
```
n=int(input())
l=list(map(int,input().split()))
for i in range(n,0,-1):
l[i-1]=sum(l[i-1::i])%2
print(sum(l))
print(*[i+1 for i in range(n) if l[i]])
``` | output | 1 | 83,999 | 16 | 167,999 |
Provide a correct Python 3 solution for this coding contest problem.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0 | instruction | 0 | 84,000 | 16 | 168,000 |
"Correct Solution:
```
N = int(input())
a = list(map(int, input().split()))
M = 0
b = [0]*N
B = []
for i in range(N, 0, -1):
wa = sum(b[i-1::i])
if wa%2 != a[i-1]:
M+=1
b[i-1] = 1
B.append(i)
print(M)
if M!=0:
print(*B)
``` | output | 1 | 84,000 | 16 | 168,001 |
Provide a correct Python 3 solution for this coding contest problem.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0 | instruction | 0 | 84,001 | 16 | 168,002 |
"Correct Solution:
```
def inpl(): return list(map(int, input().split()))
N = int(input())
A = [0] + inpl()
D = [0]*(N+1)
for i in range(N, 0, -1):
D[i] = (sum(D[2*i::i])%2)^A[i]
print(sum(D))
print(*[i for i in range(N+1) if D[i]])
``` | output | 1 | 84,001 | 16 | 168,003 |
Provide a correct Python 3 solution for this coding contest problem.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0 | instruction | 0 | 84,002 | 16 | 168,004 |
"Correct Solution:
```
N = int(input())
A = [0] + list(map(int, input().split()))
for i in range(N, 0, -1):
A[i] = sum(A[i::i]) % 2
print(sum(A))
ans = [i for i, v in enumerate(A) if v]
print(*ans)
``` | output | 1 | 84,002 | 16 | 168,005 |
Provide a correct Python 3 solution for this coding contest problem.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0 | instruction | 0 | 84,003 | 16 | 168,006 |
"Correct Solution:
```
n=int(input())
a=[0] + list(map(int,input().split()))
boxes=[0]*(n+1)
m=0
b=[]
for i in reversed(range(1,n+1)):
if sum(boxes[i::i])%2 != a[i]:
boxes[i]=1
m+=1
b.append(i)
print(m)
print(*b)
``` | output | 1 | 84,003 | 16 | 168,007 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0
Submitted Solution:
```
n = int(input())
*a, = map(int, input().split())
ans = [0] * n
for i in range(n-1, -1, -1):
if not sum(ans[i::i+1]) % 2 == a[i]:
ans[i] = 1
print(sum(ans))
print(*[i+1 for i in range(n) if ans[i] == 1])
``` | instruction | 0 | 84,004 | 16 | 168,008 |
Yes | output | 1 | 84,004 | 16 | 168,009 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0
Submitted Solution:
```
N = int(input())
A = [0] + list(map(int, input().split()))
for i in range(N, 0, -1):
A[i] = sum(A[i::i]) % 2
print(sum(A))
ans = [i for i, v in enumerate(A) if v]
print(*[i for i, v in enumerate(A) if v])
``` | instruction | 0 | 84,005 | 16 | 168,010 |
Yes | output | 1 | 84,005 | 16 | 168,011 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0
Submitted Solution:
```
n = int(input())
A = list(map(int, input().split()))
B = []
C = [0] * n
for i in reversed(range(n)):
if sum(C[i::i+1]) % 2 != A[i]:
B.append(i+1)
C[i] += 1
print(len(B))
print(' '.join(map(str, B)))
``` | instruction | 0 | 84,006 | 16 | 168,012 |
Yes | output | 1 | 84,006 | 16 | 168,013 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0
Submitted Solution:
```
N,*a = map(int,open(0).read().split())
ans = []
for i in range(N)[::-1]:
part_rem = sum(a[i::i+1]) % 2
if a[i] != part_rem:
a[i] = abs(a[i] - 1)
print(sum(a))
print(*[i+1 for i,v in enumerate(a) if v == 1])
``` | instruction | 0 | 84,007 | 16 | 168,014 |
Yes | output | 1 | 84,007 | 16 | 168,015 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0
Submitted Solution:
```
N = int(input())
A = list(map(int,input().split()))
FB = [0 for _ in range(N//2)]
SB = A[N//2:N]
B = FB + SB
S = [i for i in range(1,N//2+1)]
FH = A[0:N//2]
for i in range(1,len(FH)+1):
s = 0
for j in range(2,N//S[-i]+1):
s += B[S[-i]*j-1]
if s % 2 != FH[-i]:
FB[-i] = 1
B = FB + SB
ans = []
for i in range(N):
if B[i] == 1:
ans.append(i+1)
print(len(ans))
print(*ans)
``` | instruction | 0 | 84,008 | 16 | 168,016 |
No | output | 1 | 84,008 | 16 | 168,017 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
ans=[-1 for _ in range(n)]
for i in range(n):
j=n-i
if n//j<2:
ans[j-1]=a[j-1]
else:
p=sum(a[2*j-1::j])
ans[j-1]=abs(a[j-1]-p)
b=[0 for _ in range(sum(ans))]
i=0
#print(ans)
m=sum(ans)
print(m)
for j in range(n):
if ans[j]!=0 or ans[j]!=0:
print(-1)
exit()
if ans[j]==1:
b[i]=j+1
i+=1
print(*b)
``` | instruction | 0 | 84,009 | 16 | 168,018 |
No | output | 1 | 84,009 | 16 | 168,019 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
b = [0] * n
for i in range(n, 0, -1):
j = i
tmp = 0
while True:
j += i
if j > n:
break
tmp = (tmp + a[j-1]) // 2
b[i-1] = (tmp + a[i-1] + 1) // 2
m = sum(b)
print(m)
if m > 0:
for i in range(n):
if b[i]: print(i+1)
``` | instruction | 0 | 84,010 | 16 | 168,020 |
No | output | 1 | 84,010 | 16 | 168,021 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N empty boxes arranged in a row from left to right. The integer i is written on the i-th box from the left (1 \leq i \leq N).
For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.
We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:
* For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.
Does there exist a good set of choices? If the answer is yes, find one good set of choices.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* a_i is 0 or 1.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If a good set of choices does not exist, print `-1`.
If a good set of choices exists, print one such set of choices in the following format:
M
b_1 b_2 ... b_M
where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
a2 = [0 for _ in range(len(a))]
for a_num in range(n, 0, -1):
count = a[a_num - 1]
for i in range(1, (n + a_num - 1) // a_num):
count += a2[(a_num - 1) * i]
a2[a_num - 1] = count % 2
print(a2.count(1))
[print(i) for i in range(1, len(a2)+1) if a2[i-1] == 1]
``` | instruction | 0 | 84,011 | 16 | 168,022 |
No | output | 1 | 84,011 | 16 | 168,023 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715 | instruction | 0 | 84,028 | 16 | 168,056 |
"Correct Solution:
```
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import array
from bisect import *
from collections import *
import fractions
import heapq
from itertools import *
import math
import random
import re
import string
import sys
N, X = map(int, input().split())
Xs = list(map(int, input().split()))
Ys = Xs[::-1]
Y_sum = [0] * N
Y_sum[0] = Ys[0]
for i in range(1, N):
Y_sum[i] = Y_sum[i-1] + Ys[i]
ans = 1e100
for rep_num in range(1, N+1):
local_ans = X * rep_num
local_ans += 5 * Y_sum[rep_num - 1]
i = 2 * rep_num - 1
n = 1
while i <= N-1:
local_ans += (2 * n + 3) * (Y_sum[i] - Y_sum[i - rep_num])
n += 1
i += rep_num
local_ans += (2 * n + 3) * (Y_sum[N - 1] - Y_sum[i - rep_num])
ans = min(ans, local_ans)
print(ans + N * X)
``` | output | 1 | 84,028 | 16 | 168,057 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715 | instruction | 0 | 84,029 | 16 | 168,058 |
"Correct Solution:
```
import sys
# import numpy
N, X = map(int, input().split())
x_list = list(map(int, input().split()))
x_list.insert(0, 0)
tmp = 0
sum_x = []
for x in x_list:
tmp += x
sum_x.append(tmp)
# sum_x = numpy.cumsum(x_list)
max_robo = -(-1 * N // 2)
ans = sys.maxsize
for k in range(1, max_robo + 1):
t_ans = (N + k) * X + 5 * sum_x[N]
for j in range(1, -(-(N - k) // k)):
t_ans += 2 * sum_x[N - (j + 1) * k]
ans = min(ans, t_ans)
print(ans)
``` | output | 1 | 84,029 | 16 | 168,059 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715 | instruction | 0 | 84,030 | 16 | 168,060 |
"Correct Solution:
```
N,X=map(int,input().split())
G=list(map(int,input().split()))
S=[0]
for g in G:
S.append(S[-1]+g)
ANS=1<<60
def length(x):
if x==1:
return 5
else:
return 2*x+1
for rep in range(1,N+1):
score=X*N+X*rep
count=1
for i in range(N,0,-rep):
score+=(S[i]-S[max(0,i-rep)])*length(count)
count+=1
ANS=min(ANS,score)
print(ANS)
``` | output | 1 | 84,030 | 16 | 168,061 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715 | instruction | 0 | 84,031 | 16 | 168,062 |
"Correct Solution:
```
N, X = map(int, input().split())
gar = list(map(int, input().split()))
gar_cum = [0] * (N + 1)
for i in range(N):
gar_cum[i + 1] = gar_cum[i] + gar[i]
def move_cost(i):
#i回ゴミを捨てるときの移動コストの最小値
v = [gar_cum[N - i * j] - gar_cum[max(0, N - i * (j + 1))] for j in range((N + i - 1) // i)]
return sum([v[j] * max(5, j * 2 + 3) for j in range((N + i - 1) // i)])
def total_cost(i):
return move_cost(i) + (i + N) * X
ans = float('inf')
for i in range(1, N+1):
ans = min(ans, total_cost(i))
print(ans)
``` | output | 1 | 84,031 | 16 | 168,063 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715 | instruction | 0 | 84,032 | 16 | 168,064 |
"Correct Solution:
```
iN ,iX = [int(x) for x in input().split()]
aX = [int(x) for x in input().split()]
aCum = [0]*(iN)
aCum[0] = aX[0]
for i in range(1,iN):
aCum[i]=aCum[i-1]+aX[i]
def fCeil(iT,iR):
return -1 * iT // iR * -1
def fCalcCost(iN,iX,aCum,iK):
iCost = 5 * aCum[-1]
for i in range(2,fCeil(iN,iK) ):
iCost += 2 * aCum[-1 * i * iK -1]
iCost += (iK +iN)*iX
return iCost
iTotalCost = fCalcCost(iN,iX,aCum,1)
for iK in range(2,fCeil(iN,2) + 1):
iTotalCost = min(iTotalCost,fCalcCost(iN,iX,aCum,iK))
print(iTotalCost)
``` | output | 1 | 84,032 | 16 | 168,065 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715 | instruction | 0 | 84,033 | 16 | 168,066 |
"Correct Solution:
```
N, X = map(int, input().split())
g = list(map(int, input().split()))
s = [0]
for gi in g:
s.append(s[-1] + gi)
ans = float('inf')
for t in range(1, N + 1):
m = 5 * s[N] + t * X
for i in range(N - t * 2, 0, -t):
m += 2 * s[i]
ans = m if t == 1 else min(ans, m)
print(ans + N * X)
``` | output | 1 | 84,033 | 16 | 168,067 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715 | instruction | 0 | 84,034 | 16 | 168,068 |
"Correct Solution:
```
from itertools import accumulate
def E(i, x):
if i == 1:
return 5 * x
return (2 * i + 1) * x
N, X = map(int, input().split())
x = list(map(int, input().split()))
x.sort(key=None, reverse=True)
x = list(accumulate(x))
x.insert(0, 0)
energy = 9223372036854775807
for k in range(1, N + 1):
cost = (N + k) * X
for i in range(1, N + 1):
if i * k <= N:
cost += E(i, x[i * k] - x[(i - 1) * k])
else:
cost += E(i, x[-1] - x[(i - 1) * k])
break
if cost < energy:
energy = cost
print(energy)
``` | output | 1 | 84,034 | 16 | 168,069 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715 | instruction | 0 | 84,035 | 16 | 168,070 |
"Correct Solution:
```
N,X=map(int,input().split())
w=[0]
for i in map(int,input().split()):w+=[w[-1]+i]
print(min(5*w[N]+k*X+sum(2*w[j]for j in range(N-k*2,0,-k))for k in range(1,N+1))+N*X)
``` | output | 1 | 84,035 | 16 | 168,071 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715
Submitted Solution:
```
#!usr/bin/env python3
from collections import defaultdict
from collections import deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS():return list(map(list, sys.stdin.readline().split()))
def S(): return list(sys.stdin.readline())[:-1]
def IR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = I()
return l
def LIR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = LI()
return l
def SR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = S()
return l
def LSR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = SR()
return l
mod = 1000000007
#A
def A():
return
#B
def B():
n,X = LI()
x = LI()
for i in range(n-1):
x[i+1] += x[i]
x.insert(0,0)
ans = float("inf")
f = [5]*(n+1)
for i in range(1,n):
f[i+1] = f[i]+2
for k in range(1,n+1):
i = 0
a = n
d = (k+n)*X
while a > 0:
d += f[i]*(x[a]-x[max(0,a-k)])
a -= k
i += 1
ans = min(ans,d)
print(ans)
#C
def C():
return
#D
def D():
return
#E
def E():
return
#F
def F():
return
#G
def G():
return
#H
def H():
return
#Solve
if __name__ == "__main__":
B()
``` | instruction | 0 | 84,036 | 16 | 168,072 |
Yes | output | 1 | 84,036 | 16 | 168,073 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715
Submitted Solution:
```
def E(i, x):
if i == 1:
return 5*x
else:
return (2*i + 1) * x
N, X = map(int, input().split())
G = [int(_) for _ in input().split()]
SumG = [0 for i in range(N)]
SumG[0] = G[0]
for i in range(N-1):
SumG[i+1] = SumG[i] + G[i+1]
pick = N * X
cost = float("inf")
for k in range(1, N+1):
trush = k * X
carry = 0
i, upper, lower = 1, N-1, N-1-k
while lower >= 0:
carry += E(i, SumG[upper]-SumG[lower])
i, upper, lower = i+1, lower, lower - k
carry += E(i, SumG[upper])
cost = min(cost, pick + trush + carry)
print(cost)
``` | instruction | 0 | 84,037 | 16 | 168,074 |
Yes | output | 1 | 84,037 | 16 | 168,075 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715
Submitted Solution:
```
N, X = list(map(int, input().split()))
x = list(map(int, input().split()))
D = [pow(i, 2) for i in range(1, N + 2)]
ok = N
ng = 1
List = [-1 for i in range(N + 1)]
while abs(ok - ng) > 2:
LR = [(ok - ng) // 3 + ng, 2 * (ok - ng) // 3 + ng]
Ans = [0, 0]
for j in range(2):
if List[LR[j]] != -1:
Ans[j] = List[LR[j]]
continue
least = 0
Ans[j] = X * (N + LR[j])
cnt = -1
t = 0
flag = False
for i in x[::-1]:
if flag:
Ans[j] += (D[least + 1] - D[least]) * x[cnt]
else:
Ans[j] += (D[0] + D[1]) * x[cnt]
cnt -= 1
t += 1
if t == LR[j]:
t = 0
least += 1
flag = True
List[LR[j]] = Ans[j]
if Ans[0] < Ans[1]:
ok = LR[1]
else:
ng = LR[0]
FA = 1e20
for j in range(ng, ok + 1):
if List[j] != -1:
FA = min(FA, List[j])
continue
least = 0
Ans = X * (N + j)
cnt = -1
t = 0
flag = False
for i in x[::-1]:
if flag:
Ans += (D[least + 1] - D[least]) * x[cnt]
else:
Ans += (D[0] + D[1]) * x[cnt]
cnt -= 1
t += 1
if t == j:
t = 0
least += 1
flag = True
FA = min(FA, Ans)
print(FA)
``` | instruction | 0 | 84,038 | 16 | 168,076 |
Yes | output | 1 | 84,038 | 16 | 168,077 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715
Submitted Solution:
```
I=lambda:map(int,input().split())
n,p = I()
s=[0]
for i in I():
s += [s[-1] + i]
for t in range(1, n + 1):
m = 5 * s[n] + t * p
c = n - t * 2
while c > 0:
m += 2 * s[c]
c -= t
a = m if t == 1 else min(a,m)
print(a + n * p)
``` | instruction | 0 | 84,039 | 16 | 168,078 |
Yes | output | 1 | 84,039 | 16 | 168,079 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715
Submitted Solution:
```
N, X=map(int, input().split())
x=[]
x=list(map(int, input().split()))
A=0
B=0
C=0
for i in range(N-2):
A=A+(N-2)*x[i]
for j in range(N):
C=C+5*x[j]
if X<=A:
B=C+X
else:
B=C+A
print(B)
``` | instruction | 0 | 84,040 | 16 | 168,080 |
No | output | 1 | 84,040 | 16 | 168,081 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715
Submitted Solution:
```
N,X = [int(i) for i in input().split()]
x = [int(i) for i in input().split()]
x.insert(0,0)
x.reverse()
table = [[0 for i in range(N+5)]for j in [0,1] ]
table[0][0] = 0
a = False
for i in range(N):
for j in range(i):
table[not(a)][j+1] = table[a][j] + (j+2)*(j+2)*(x[j] - x[j+1]) + X
table[not(a)][0] = table[a][i-1] + (i+1)*(i+1)*x[i-1] + x[i] + X
a = not(a)
print(table[a])
ans = 10000000000000000000000
for i in range(N):
ans = min(ans, table[a][i] + (i+2)*(i+2) * x[N-1] + X)
print(ans)
``` | instruction | 0 | 84,041 | 16 | 168,082 |
No | output | 1 | 84,041 | 16 | 168,083 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715
Submitted Solution:
```
from collections import deque
n,x=map(int,input().split())
line=list(map(int,input().split()))
line=deque(line)
ans=0
if len(line)%2!=0:
if line[0]*2<x:
ans+=line.popleft()*7
ans+=x
else:
ans+=line.popleft()*5
ans+=x*2
p=len(line)//2
while 2<p:
if line[0]*7+line[1]*7<x:
ans+=line.popleft()*7+line.popleft()*7
ans+=x*2
p-=3
while len(line)>0:
ans+=line.pop()*5
ans+=line.pop()*5
ans+=x*3
print(ans)
``` | instruction | 0 | 84,042 | 16 | 168,084 |
No | output | 1 | 84,042 | 16 | 168,085 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715
Submitted Solution:
```
N, X = map(int, input().split())
xs = list(map(int, input().split()))
dp = []
dp.append(5 * xs[0] + 2 * X)
dp.append(5 * (xs[0] + xs[1]) + 3 * X)
costA = dp[-1]
v = 2 * xs[0]
for i in range(2, N):
# min(
# 全部拾って帰る,
# 1個前の最小値 + i個目を拾う,
# 2個前の最小値 + i,i-1個目を拾う
# )
costA = costA + 5 * xs[i] + v + X
costB = dp[-1] + 5 * xs[i] + 2 * X
costC = dp[-2] + 5 * (xs[i] + xs[i-1]) + 3 * X
dp.append(min(costA, costB, costC))
v += 2 * xs[i-1]
print(dp[-1])
``` | instruction | 0 | 84,043 | 16 | 168,086 |
No | output | 1 | 84,043 | 16 | 168,087 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has X+Y balls. X of them have an integer A written on them, and the other Y of them have an integer B written on them.
Snuke will divide these balls into some number of groups. Here, every ball should be contained in exactly one group, and every group should contain one or more balls.
A group is said to be good when the sum of the integers written on the balls in that group is a multiple of an integer C. Find the maximum possible number of good groups.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 2 \times 10^4
* 1 \leq A,X,B,Y,C \leq 10^9
* A \neq B
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
A X B Y C
Output
For each test case, print a line containing the maximum possible number of good groups.
Example
Input
3
3 3 4 4 5
2 1 1 5 3
3 1 4 2 5
Output
2
2
0
Submitted Solution:
```
T = int(input())
#NumList=[3, 3, 4, 4, 5]
NumList=[2, 1, 1, 5, 3]
P = [input().split() for i in range(T)]
def ReturnGoodGroup(AXBYC):
NumList=AXBYC
A, X, B, Y, C = int(NumList[0]),int(NumList[1]),int(NumList[2]),int(NumList[3]),int(NumList[4])
RemainingBall=X+Y
GroupNum=0
BallList=[]
for A_times in range(X+1):
for B_times in range(Y+1):
if A_times+B_times>0 and (A*A_times+B*B_times)%C==0:
BallList.append([A_times,B_times])
OmomiBallList=[[x[0]/A,x[0]/B] for x in BallList]
#print(OmomiBallList)
BallNumSumList=[sum(x) for x in OmomiBallList]
OmomiSortedBallList = [x for _,x in sorted(zip(BallNumSumList,BallList))]
#print(OmomiSortedBallList)
A_Remain=X
B_Remain=Y
for ls in OmomiSortedBallList:
#print(ls)
A_Remain-=ls[0]
B_Remain-=ls[1]
# print("A_Remain:")
# print(A_Remain)
# print("B_Remain:")
# print(B_Remain)
if A_Remain>-1 and B_Remain>-1:
GroupNum+=1
elif A_Remain<0 or B_Remain<0:
break
return(GroupNum)
for AXBYC in P:
print(ReturnGoodGroup(AXBYC))
``` | instruction | 0 | 84,802 | 16 | 169,604 |
No | output | 1 | 84,802 | 16 | 169,605 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has X+Y balls. X of them have an integer A written on them, and the other Y of them have an integer B written on them.
Snuke will divide these balls into some number of groups. Here, every ball should be contained in exactly one group, and every group should contain one or more balls.
A group is said to be good when the sum of the integers written on the balls in that group is a multiple of an integer C. Find the maximum possible number of good groups.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 2 \times 10^4
* 1 \leq A,X,B,Y,C \leq 10^9
* A \neq B
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
A X B Y C
Output
For each test case, print a line containing the maximum possible number of good groups.
Example
Input
3
3 3 4 4 5
2 1 1 5 3
3 1 4 2 5
Output
2
2
0
Submitted Solution:
```
import sys
from collections import deque
import itertools
def I(): return int(sys.stdin.readline().rstrip())
def LI():return list(map(int,sys.stdin.readline().rstrip().split()))
def LS():return list(sys.stdin.readline().rstrip().split())
def a(target, a, b, x, y):
# print("target=",target,"a=",a,"b=",b,"x=",x,"y=",y)
a_n = min(x, target // a)
b_n = min(y, target // b)
# print("a_n=",a_n, "target//a=",target//a, "b_n=",b_n,"target//b=",target//b)
comb = []
for a_i in range(a_n+1):
for b_i in range(b_n+1):
s = a * a_i + b * b_i
# print("target=",target,"a=",a_i,"b=",b_i,"s=",s)
if s == target:
comb.append((a_i,b_i))
return comb
def solver():
A,X,B,Y,C = LI()
# print("A=",A)
# print("X=",X)
# print("B=",B)
# print("Y=",Y)
# print("C=",C)
Total = A*X+B*Y
C_loop = Total//C
a_lmt = X
b_lmt = Y
ans = 0
for c_i in range(C_loop):
C_target = C * (c_i+1)
pattern = a(C_target, A, B, a_lmt, b_lmt)
print("target=",C_target, "pattern_num=",len(pattern))
ans += len(pattern)
for p in pattern:
# print("p=",p)
a_lmt -= p[0]
b_lmt -= p[1]
return ans
def main():
T = I()
# print("T=",T)
for _ in range(T):
# print("ANS=",solver())
print(solver())
if __name__ == '__main__':
main()
``` | instruction | 0 | 84,803 | 16 | 169,606 |
No | output | 1 | 84,803 | 16 | 169,607 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has X+Y balls. X of them have an integer A written on them, and the other Y of them have an integer B written on them.
Snuke will divide these balls into some number of groups. Here, every ball should be contained in exactly one group, and every group should contain one or more balls.
A group is said to be good when the sum of the integers written on the balls in that group is a multiple of an integer C. Find the maximum possible number of good groups.
Solve T test cases for each input file.
Constraints
* 1 \leq T \leq 2 \times 10^4
* 1 \leq A,X,B,Y,C \leq 10^9
* A \neq B
Input
Input is given from Standard Input in the following format. The first line is as follows:
T
Then, T test cases follow. Each test case is given in the following format:
A X B Y C
Output
For each test case, print a line containing the maximum possible number of good groups.
Example
Input
3
3 3 4 4 5
2 1 1 5 3
3 1 4 2 5
Output
2
2
0
Submitted Solution:
```
import sys
from collections import deque
import itertools
def I(): return int(sys.stdin.readline().rstrip())
def LI():return list(map(int,sys.stdin.readline().rstrip().split()))
def LS():return list(sys.stdin.readline().rstrip().split())
def a(target, a, b, x, y):
# print("target=",target,"a=",a,"b=",b,"x=",x,"y=",y)
a_n = min(x, target // a)
b_n = min(y, target // b)
# print("a_n=",a_n, "target//a=",target//a, "b_n=",b_n,"target//b=",target//b)
comb = []
for a_i in range(a_n+1):
for b_i in range(b_n+1):
s = a * a_i + b * b_i
# print("target=",target,"a=",a_i,"b=",b_i,"s=",s)
if s == target:
comb.append((a_i,b_i))
return comb
def solver():
A,X,B,Y,C = LI()
# print("A=",A)
# print("X=",X)
# print("B=",B)
# print("Y=",Y)
# print("C=",C)
Total = A*X+B*Y
C_loop = Total//C
a_lmt = X
b_lmt = Y
ans = 0
for c_i in range(C_loop):
C_target = C * (c_i+1)
pattern = a(C_target, A, B, a_lmt, b_lmt)
# print("target=",C_target, "pattern_num=",len(pattern))
ans += len(pattern)
for p in pattern:
# print("p=",p)
a_lmt -= p[0]
b_lmt -= p[1]
return ans
def main():
T = I()
# print("T=",T)
for _ in range(T):
# print("ANS=",solver())
print(solver())
if __name__ == '__main__':
main()
``` | instruction | 0 | 84,804 | 16 | 169,608 |
No | output | 1 | 84,804 | 16 | 169,609 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8 | instruction | 0 | 85,595 | 16 | 171,190 |
"Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
c = 0
while all(i % 2 == 0 for i in A):
A = [i/2 for i in A]
c += 1
print(c)
``` | output | 1 | 85,595 | 16 | 171,191 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8 | instruction | 0 | 85,596 | 16 | 171,192 |
"Correct Solution:
```
n=int(input())
*a,=map(int,input().split())
c=0
while all([i%2==0 for i in a]):
a=[j/2 for j in a]
c+=1
print(c)
``` | output | 1 | 85,596 | 16 | 171,193 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8 | instruction | 0 | 85,597 | 16 | 171,194 |
"Correct Solution:
```
input()
n = eval(input().replace(' ', '|'))
for i in range(201):
if n & 1 << i:
print(i)
break
``` | output | 1 | 85,597 | 16 | 171,195 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8 | instruction | 0 | 85,598 | 16 | 171,196 |
"Correct Solution:
```
input()
A=list(map(int,input().split()))
index = 0
while all (a%2 == 0 for a in A):
A = [a/2 for a in A]
index += 1
print(index)
``` | output | 1 | 85,598 | 16 | 171,197 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8 | instruction | 0 | 85,599 | 16 | 171,198 |
"Correct Solution:
```
n=int(input())
l=list(map(int,input().split()))
count=0
while all(i%2==0 for i in l):
l=[i/2 for i in l]
count+=1
print(count)
``` | output | 1 | 85,599 | 16 | 171,199 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8 | instruction | 0 | 85,600 | 16 | 171,200 |
"Correct Solution:
```
input()
n=eval(input().replace(' ','|'))
print(len(bin(n&-n))-3)
``` | output | 1 | 85,600 | 16 | 171,201 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8 | instruction | 0 | 85,601 | 16 | 171,202 |
"Correct Solution:
```
input()
a=list(map(int, input().split()))
count=0
while all(x%2==0 for x in a):
a=[x/2 for x in a]
count+=1
print(count)
``` | output | 1 | 85,601 | 16 | 171,203 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8 | instruction | 0 | 85,602 | 16 | 171,204 |
"Correct Solution:
```
_ = input()
a = [int(x) for x in input().split()]
f = lambda x : len(bin(x & -x)[2:].split('1')[-1])
print(min([f(x) for x in a]))
``` | output | 1 | 85,602 | 16 | 171,205 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
ans=30
for i in a:
ans=min(ans,len(bin(i))-bin(i).rfind("1")-1)
print(ans)
``` | instruction | 0 | 85,603 | 16 | 171,206 |
Yes | output | 1 | 85,603 | 16 | 171,207 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
ans=0
while all(aa%2==0 for aa in a):
ans+=1
a=[aa//2 for aa in a]
print(ans)
``` | instruction | 0 | 85,604 | 16 | 171,208 |
Yes | output | 1 | 85,604 | 16 | 171,209 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8
Submitted Solution:
```
N = int(input())
A = [int(x) for x in input().split()]
import math
mn = min(x & (-x) for x in A)
print(int(math.log(mn, 2)))
``` | instruction | 0 | 85,605 | 16 | 171,210 |
Yes | output | 1 | 85,605 | 16 | 171,211 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8
Submitted Solution:
```
def f(x):
x=int(x)
res = 0
while x % 2 == 0:
x //= 2
res += 1
return res
input()
print(min(map(f,input().split())))
``` | instruction | 0 | 85,606 | 16 | 171,212 |
Yes | output | 1 | 85,606 | 16 | 171,213 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8
Submitted Solution:
```
import math
s = list(map(int, input().split()))
ans = float('inf')
for i in s:
ans = min(ans, len(bin(i)) - bin(i).rfind("1") - 1)
print(ans)
``` | instruction | 0 | 85,607 | 16 | 171,214 |
No | output | 1 | 85,607 | 16 | 171,215 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8
Submitted Solution:
```
num = int(input())
a = list(map(int, input().split()))
av_count = 0
out_count = 0
for i in a:
if i % 2 == 0:
av_count += 1
else:
pass
if num == av_count:
for j in a:
j /= 2
out_count += 1
print(out_count)
``` | instruction | 0 | 85,608 | 16 | 171,216 |
No | output | 1 | 85,608 | 16 | 171,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8
Submitted Solution:
```
N = int(input())
A = list(map(int, input().split()))
ans = 0
while len(A) == N:
A = [a for a in A if a % 2 == 0]
if len(A) == N:
ans += 1
print(ans)
``` | instruction | 0 | 85,609 | 16 | 171,218 |
No | output | 1 | 85,609 | 16 | 171,219 |
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