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.
Dreamoon likes sequences very much. So he created a problem about the sequence that you can't find in OEIS:
You are given two integers d, m, find the number of arrays a, satisfying the following constraints:
* The length of a is n, n ≥ 1
* 1 ≤ a_1 < a_2 < ... < a_n ≤ d
* Define an array b of length n as follows: b_1 = a_1, ∀ i > 1, b_i = b_{i - 1} ⊕ a_i, where ⊕ is the bitwise exclusive-or (xor). After constructing an array b, the constraint b_1 < b_2 < ... < b_{n - 1} < b_n should hold.
Since the number of possible arrays may be too large, you need to find the answer modulo m.
Input
The first line contains an integer t (1 ≤ t ≤ 100) denoting the number of test cases in the input.
Each of the next t lines contains two integers d, m (1 ≤ d, m ≤ 10^9).
Note that m is not necessary the prime!
Output
For each test case, print the number of arrays a, satisfying all given constrains, modulo m.
Example
Input
10
1 1000000000
2 999999999
3 99999998
4 9999997
5 999996
6 99995
7 9994
8 993
9 92
10 1
Output
1
3
5
11
17
23
29
59
89
0
Submitted Solution:
```
import math
t = int(input())
while (t):
line = input().split()
d,m = int(line[0]), int(line[1])
if (d == 1):
print(1 % m)
elif (d == 2):
print(3 % m)
else:
k = int(math.log(d)/math.log(2))
f = 1
#print(k)
for i in range(1,k+1):
#print('f =', f, '*', (1<<(i-1))+1)
f = (f * ((1 << (i-1)) + 1)) % m
#print('f =', f,'+',(1<<(i-1)))
f = (f + (1 << (i-1))) % m
#print(i,f)
#print(f)
a = (d - (1 << k)) % m
b = (f+1)
if (m % 2 == 0):
if (b < 2*m):
b //= 2
else:
b = (b % m) // 2
else:
b = b * (m//2+1)
print((a*b + f) % m)
t -= 1
``` | instruction | 0 | 53,233 | 5 | 106,466 |
No | output | 1 | 53,233 | 5 | 106,467 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes sequences very much. So he created a problem about the sequence that you can't find in OEIS:
You are given two integers d, m, find the number of arrays a, satisfying the following constraints:
* The length of a is n, n ≥ 1
* 1 ≤ a_1 < a_2 < ... < a_n ≤ d
* Define an array b of length n as follows: b_1 = a_1, ∀ i > 1, b_i = b_{i - 1} ⊕ a_i, where ⊕ is the bitwise exclusive-or (xor). After constructing an array b, the constraint b_1 < b_2 < ... < b_{n - 1} < b_n should hold.
Since the number of possible arrays may be too large, you need to find the answer modulo m.
Input
The first line contains an integer t (1 ≤ t ≤ 100) denoting the number of test cases in the input.
Each of the next t lines contains two integers d, m (1 ≤ d, m ≤ 10^9).
Note that m is not necessary the prime!
Output
For each test case, print the number of arrays a, satisfying all given constrains, modulo m.
Example
Input
10
1 1000000000
2 999999999
3 99999998
4 9999997
5 999996
6 99995
7 9994
8 993
9 92
10 1
Output
1
3
5
11
17
23
29
59
89
0
Submitted Solution:
```
lis=[1,2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229]
import math
for _ in range(int(input())):
a,b = map(int,input().split())
ans=p=k=aa=0
prev=1
while k<a:
p=min(pow(2,aa),a-k)
ans+=(p*(lis[aa]*prev))
k+=p
prev*=lis[aa]
aa+=1
print(ans%b)
``` | instruction | 0 | 53,234 | 5 | 106,468 |
No | output | 1 | 53,234 | 5 | 106,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Slime has a sequence of positive integers a_1, a_2, …, a_n.
In one operation Orac can choose an arbitrary subsegment [l … r] of this sequence and replace all values a_l, a_{l + 1}, …, a_r to the value of median of \\{a_l, a_{l + 1}, …, a_r\}.
In this problem, for the integer multiset s, the median of s is equal to the ⌊ (|s|+1)/(2)⌋-th smallest number in it. For example, the median of \{1,4,4,6,5\} is 4, and the median of \{1,7,5,8\} is 5.
Slime wants Orac to make a_1 = a_2 = … = a_n = k using these operations.
Orac thinks that it is impossible, and he does not want to waste his time, so he decided to ask you if it is possible to satisfy the Slime's requirement, he may ask you these questions several times.
Input
The first line of the input is a single integer t: the number of queries.
The first line of each query contains two integers n\ (1≤ n≤ 100 000) and k\ (1≤ k≤ 10^9), the second line contains n positive integers a_1,a_2,...,a_n\ (1≤ a_i≤ 10^9)
The total sum of n is at most 100 000.
Output
The output should contain t lines. The i-th line should be equal to 'yes' if it is possible to make all integers k in some number of operations or 'no', otherwise. You can print each letter in lowercase or uppercase.
Example
Input
5
5 3
1 5 2 6 1
1 6
6
3 2
1 2 3
4 3
3 1 2 3
10 3
1 2 3 4 5 6 7 8 9 10
Output
no
yes
yes
no
yes
Note
In the first query, Orac can't turn all elements into 3.
In the second query, a_1=6 is already satisfied.
In the third query, Orac can select the complete array and turn all elements into 2.
In the fourth query, Orac can't turn all elements into 3.
In the fifth query, Orac can select [1,6] at first and then select [2,10].
Submitted Solution:
```
from bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush,heappop
import math
from collections import *
from functools import reduce,cmp_to_key,lru_cache
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# import sys
# input = sys.stdin.readline
M = mod = 10**9 + 7
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
def inv_mod(n):return pow(n, mod - 2, mod)
def li():return [int(i) for i in input().rstrip().split()]
def st():return str(input().rstrip())[2:-1]
def val():return int(input().rstrip())
def li2():return [str(i)[2:-1] for i in input().rstrip().split()]
def li3():return [int(str(i)[2:-1]) for i in input().rstrip()]
def do2(l):
n = len(l)
for i in range(2,n + 1):
if sum(l[i-2:i + 1]) > 0 or sum(l[i-2:i]) > 0:return 1
return 0
for _ in range(val()):
n,k = li()
l = li()
if k not in l:
print('NO')
continue
if n == 1:
print('YES')
continue
l = [(-1 if i < k else 1) for i in l]
print('YES' if do2(l) else 'NO')
``` | instruction | 0 | 53,243 | 5 | 106,486 |
Yes | output | 1 | 53,243 | 5 | 106,487 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Slime has a sequence of positive integers a_1, a_2, …, a_n.
In one operation Orac can choose an arbitrary subsegment [l … r] of this sequence and replace all values a_l, a_{l + 1}, …, a_r to the value of median of \\{a_l, a_{l + 1}, …, a_r\}.
In this problem, for the integer multiset s, the median of s is equal to the ⌊ (|s|+1)/(2)⌋-th smallest number in it. For example, the median of \{1,4,4,6,5\} is 4, and the median of \{1,7,5,8\} is 5.
Slime wants Orac to make a_1 = a_2 = … = a_n = k using these operations.
Orac thinks that it is impossible, and he does not want to waste his time, so he decided to ask you if it is possible to satisfy the Slime's requirement, he may ask you these questions several times.
Input
The first line of the input is a single integer t: the number of queries.
The first line of each query contains two integers n\ (1≤ n≤ 100 000) and k\ (1≤ k≤ 10^9), the second line contains n positive integers a_1,a_2,...,a_n\ (1≤ a_i≤ 10^9)
The total sum of n is at most 100 000.
Output
The output should contain t lines. The i-th line should be equal to 'yes' if it is possible to make all integers k in some number of operations or 'no', otherwise. You can print each letter in lowercase or uppercase.
Example
Input
5
5 3
1 5 2 6 1
1 6
6
3 2
1 2 3
4 3
3 1 2 3
10 3
1 2 3 4 5 6 7 8 9 10
Output
no
yes
yes
no
yes
Note
In the first query, Orac can't turn all elements into 3.
In the second query, a_1=6 is already satisfied.
In the third query, Orac can select the complete array and turn all elements into 2.
In the fourth query, Orac can't turn all elements into 3.
In the fifth query, Orac can select [1,6] at first and then select [2,10].
Submitted Solution:
```
import sys
input = sys.stdin.readline
t = int(input())
for _ in range(t):
n, k = map(int, input().split())
a = list(map(int, input().split()))
now = -1
if k not in a:
print('no')
continue
if len(a)==1:
print('yes')
continue
for i in a:
if i==k and now>=0:
print('yes')
break
if i>=k:
if now < 0:
now = 1
else:
print('yes')
break
else:
now -= 1
else:
now = -1
for i in reversed(a):
if i==k and now>=0:
print('yes')
break
if i>=k:
now = max(1, now+1)
else:
now -= 1
else:
print('no')
``` | instruction | 0 | 53,244 | 5 | 106,488 |
Yes | output | 1 | 53,244 | 5 | 106,489 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Slime has a sequence of positive integers a_1, a_2, …, a_n.
In one operation Orac can choose an arbitrary subsegment [l … r] of this sequence and replace all values a_l, a_{l + 1}, …, a_r to the value of median of \\{a_l, a_{l + 1}, …, a_r\}.
In this problem, for the integer multiset s, the median of s is equal to the ⌊ (|s|+1)/(2)⌋-th smallest number in it. For example, the median of \{1,4,4,6,5\} is 4, and the median of \{1,7,5,8\} is 5.
Slime wants Orac to make a_1 = a_2 = … = a_n = k using these operations.
Orac thinks that it is impossible, and he does not want to waste his time, so he decided to ask you if it is possible to satisfy the Slime's requirement, he may ask you these questions several times.
Input
The first line of the input is a single integer t: the number of queries.
The first line of each query contains two integers n\ (1≤ n≤ 100 000) and k\ (1≤ k≤ 10^9), the second line contains n positive integers a_1,a_2,...,a_n\ (1≤ a_i≤ 10^9)
The total sum of n is at most 100 000.
Output
The output should contain t lines. The i-th line should be equal to 'yes' if it is possible to make all integers k in some number of operations or 'no', otherwise. You can print each letter in lowercase or uppercase.
Example
Input
5
5 3
1 5 2 6 1
1 6
6
3 2
1 2 3
4 3
3 1 2 3
10 3
1 2 3 4 5 6 7 8 9 10
Output
no
yes
yes
no
yes
Note
In the first query, Orac can't turn all elements into 3.
In the second query, a_1=6 is already satisfied.
In the third query, Orac can select the complete array and turn all elements into 2.
In the fourth query, Orac can't turn all elements into 3.
In the fifth query, Orac can select [1,6] at first and then select [2,10].
Submitted Solution:
```
def main():
t = int(input())
for _ in range(t):
n, k = map(int, input().split())
a = list(map(int, input().split()))
if k not in a:
print("no")
continue
if n == 1:
print("yes")
continue
bl = False
for i in range(n):
if a[i] < k:
continue
for j in range(i + 1, min(i + 3, n)):
if a[j] >= k:
bl = True
print("yes" if bl else "no")
if __name__ == "__main__":
main()
``` | instruction | 0 | 53,245 | 5 | 106,490 |
Yes | output | 1 | 53,245 | 5 | 106,491 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Slime has a sequence of positive integers a_1, a_2, …, a_n.
In one operation Orac can choose an arbitrary subsegment [l … r] of this sequence and replace all values a_l, a_{l + 1}, …, a_r to the value of median of \\{a_l, a_{l + 1}, …, a_r\}.
In this problem, for the integer multiset s, the median of s is equal to the ⌊ (|s|+1)/(2)⌋-th smallest number in it. For example, the median of \{1,4,4,6,5\} is 4, and the median of \{1,7,5,8\} is 5.
Slime wants Orac to make a_1 = a_2 = … = a_n = k using these operations.
Orac thinks that it is impossible, and he does not want to waste his time, so he decided to ask you if it is possible to satisfy the Slime's requirement, he may ask you these questions several times.
Input
The first line of the input is a single integer t: the number of queries.
The first line of each query contains two integers n\ (1≤ n≤ 100 000) and k\ (1≤ k≤ 10^9), the second line contains n positive integers a_1,a_2,...,a_n\ (1≤ a_i≤ 10^9)
The total sum of n is at most 100 000.
Output
The output should contain t lines. The i-th line should be equal to 'yes' if it is possible to make all integers k in some number of operations or 'no', otherwise. You can print each letter in lowercase or uppercase.
Example
Input
5
5 3
1 5 2 6 1
1 6
6
3 2
1 2 3
4 3
3 1 2 3
10 3
1 2 3 4 5 6 7 8 9 10
Output
no
yes
yes
no
yes
Note
In the first query, Orac can't turn all elements into 3.
In the second query, a_1=6 is already satisfied.
In the third query, Orac can select the complete array and turn all elements into 2.
In the fourth query, Orac can't turn all elements into 3.
In the fifth query, Orac can select [1,6] at first and then select [2,10].
Submitted Solution:
```
import sys
input=sys.stdin.readline
def main():
n,k=map(int,input().split())
A=list(map(int,input().split()))
if min(A) == max(A) == k:
print('yes')
return
if k not in A:
print('no')
return
A = [x >= k for x in A] + [0, 0]
print('yes' if max(sum(A[i:i+3]) for i in range(n)) > 1 else 'no')
T=int(input())
for _ in range(T):
main()
``` | instruction | 0 | 53,246 | 5 | 106,492 |
Yes | output | 1 | 53,246 | 5 | 106,493 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Slime has a sequence of positive integers a_1, a_2, …, a_n.
In one operation Orac can choose an arbitrary subsegment [l … r] of this sequence and replace all values a_l, a_{l + 1}, …, a_r to the value of median of \\{a_l, a_{l + 1}, …, a_r\}.
In this problem, for the integer multiset s, the median of s is equal to the ⌊ (|s|+1)/(2)⌋-th smallest number in it. For example, the median of \{1,4,4,6,5\} is 4, and the median of \{1,7,5,8\} is 5.
Slime wants Orac to make a_1 = a_2 = … = a_n = k using these operations.
Orac thinks that it is impossible, and he does not want to waste his time, so he decided to ask you if it is possible to satisfy the Slime's requirement, he may ask you these questions several times.
Input
The first line of the input is a single integer t: the number of queries.
The first line of each query contains two integers n\ (1≤ n≤ 100 000) and k\ (1≤ k≤ 10^9), the second line contains n positive integers a_1,a_2,...,a_n\ (1≤ a_i≤ 10^9)
The total sum of n is at most 100 000.
Output
The output should contain t lines. The i-th line should be equal to 'yes' if it is possible to make all integers k in some number of operations or 'no', otherwise. You can print each letter in lowercase or uppercase.
Example
Input
5
5 3
1 5 2 6 1
1 6
6
3 2
1 2 3
4 3
3 1 2 3
10 3
1 2 3 4 5 6 7 8 9 10
Output
no
yes
yes
no
yes
Note
In the first query, Orac can't turn all elements into 3.
In the second query, a_1=6 is already satisfied.
In the third query, Orac can select the complete array and turn all elements into 2.
In the fourth query, Orac can't turn all elements into 3.
In the fifth query, Orac can select [1,6] at first and then select [2,10].
Submitted Solution:
```
import math as mt
import sys,string
input=sys.stdin.readline
import random
from collections import deque,defaultdict
L=lambda : list(map(int,input().split()))
Ls=lambda : list(input().split())
M=lambda : map(int,input().split())
I=lambda :int(input())
def lcm(a,b):
return (a*b)//mt.gcd(a,b)
t=I()
for _ in range(t):
n,k=M()
l=L()
f=0
if(n==1):
if(l[0]==k):
print("yes")
else:
print("no")
else:
for i in range(n-1):
if(sorted(l[i:i+2])[0]==k):
f=1
break
if(f==0):
for i in range(n-2):
if(sorted(l[i:i+3])[1]==k):
f=1
break
if(f):
print("yes")
else:
print("no")
``` | instruction | 0 | 53,247 | 5 | 106,494 |
No | output | 1 | 53,247 | 5 | 106,495 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Slime has a sequence of positive integers a_1, a_2, …, a_n.
In one operation Orac can choose an arbitrary subsegment [l … r] of this sequence and replace all values a_l, a_{l + 1}, …, a_r to the value of median of \\{a_l, a_{l + 1}, …, a_r\}.
In this problem, for the integer multiset s, the median of s is equal to the ⌊ (|s|+1)/(2)⌋-th smallest number in it. For example, the median of \{1,4,4,6,5\} is 4, and the median of \{1,7,5,8\} is 5.
Slime wants Orac to make a_1 = a_2 = … = a_n = k using these operations.
Orac thinks that it is impossible, and he does not want to waste his time, so he decided to ask you if it is possible to satisfy the Slime's requirement, he may ask you these questions several times.
Input
The first line of the input is a single integer t: the number of queries.
The first line of each query contains two integers n\ (1≤ n≤ 100 000) and k\ (1≤ k≤ 10^9), the second line contains n positive integers a_1,a_2,...,a_n\ (1≤ a_i≤ 10^9)
The total sum of n is at most 100 000.
Output
The output should contain t lines. The i-th line should be equal to 'yes' if it is possible to make all integers k in some number of operations or 'no', otherwise. You can print each letter in lowercase or uppercase.
Example
Input
5
5 3
1 5 2 6 1
1 6
6
3 2
1 2 3
4 3
3 1 2 3
10 3
1 2 3 4 5 6 7 8 9 10
Output
no
yes
yes
no
yes
Note
In the first query, Orac can't turn all elements into 3.
In the second query, a_1=6 is already satisfied.
In the third query, Orac can select the complete array and turn all elements into 2.
In the fourth query, Orac can't turn all elements into 3.
In the fifth query, Orac can select [1,6] at first and then select [2,10].
Submitted Solution:
```
# from functools import lru_cache
from sys import stdin, stdout
# import sys
from math import *
# sys.setrecursionlimit(10**6)
input = stdin.readline
# print = stdout.write
# @lru_cache()
for i in range(int(input())):
n,k=map(int,input().split())
ar=list(map(int,input().split()))
if(n==1):
print("yes")
elif(n==2):
if(ar[1]==k):
print("yes")
else:
print("no")
else:
ans="no"
for i in range(1,n-1):
if(ar[i]==k):
ans="yes"
print(ans)
``` | instruction | 0 | 53,248 | 5 | 106,496 |
No | output | 1 | 53,248 | 5 | 106,497 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Slime has a sequence of positive integers a_1, a_2, …, a_n.
In one operation Orac can choose an arbitrary subsegment [l … r] of this sequence and replace all values a_l, a_{l + 1}, …, a_r to the value of median of \\{a_l, a_{l + 1}, …, a_r\}.
In this problem, for the integer multiset s, the median of s is equal to the ⌊ (|s|+1)/(2)⌋-th smallest number in it. For example, the median of \{1,4,4,6,5\} is 4, and the median of \{1,7,5,8\} is 5.
Slime wants Orac to make a_1 = a_2 = … = a_n = k using these operations.
Orac thinks that it is impossible, and he does not want to waste his time, so he decided to ask you if it is possible to satisfy the Slime's requirement, he may ask you these questions several times.
Input
The first line of the input is a single integer t: the number of queries.
The first line of each query contains two integers n\ (1≤ n≤ 100 000) and k\ (1≤ k≤ 10^9), the second line contains n positive integers a_1,a_2,...,a_n\ (1≤ a_i≤ 10^9)
The total sum of n is at most 100 000.
Output
The output should contain t lines. The i-th line should be equal to 'yes' if it is possible to make all integers k in some number of operations or 'no', otherwise. You can print each letter in lowercase or uppercase.
Example
Input
5
5 3
1 5 2 6 1
1 6
6
3 2
1 2 3
4 3
3 1 2 3
10 3
1 2 3 4 5 6 7 8 9 10
Output
no
yes
yes
no
yes
Note
In the first query, Orac can't turn all elements into 3.
In the second query, a_1=6 is already satisfied.
In the third query, Orac can select the complete array and turn all elements into 2.
In the fourth query, Orac can't turn all elements into 3.
In the fifth query, Orac can select [1,6] at first and then select [2,10].
Submitted Solution:
```
t = int(input())
out = []
for i in range(t):
n, k = [int(x) for x in input().split()]
arr = [int(x) for x in input().split()]
if k not in arr:
out.append('no')
elif n == 1 and arr[0] == k:
out.append('yes')
elif n == 1 and arr[0] != k:
out.append('no')
elif k in arr:
if k == arr[0] and arr.count(k) == 1:
if arr[1] >= arr[0]:
out.append('yes')
else:
out.append('no')
elif k == arr[n - 1] and arr.count(k) == 1:
if arr[n - 2] >= arr[n - 1]:
out.append('yes')
else:
out.append('no')
elif k == arr[0] and k == arr[n - 1] and arr.count(k) == 2:
if arr[1] >= arr[0] or arr[n - 2] >= arr[n - 1]:
out.append('yes')
elif arr[1] < arr[0] and arr[n - 2] < arr[n - 1]:
out.append('no')
else:
out.append('yes')
for ans in out:
print(ans)
``` | instruction | 0 | 53,249 | 5 | 106,498 |
No | output | 1 | 53,249 | 5 | 106,499 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Slime has a sequence of positive integers a_1, a_2, …, a_n.
In one operation Orac can choose an arbitrary subsegment [l … r] of this sequence and replace all values a_l, a_{l + 1}, …, a_r to the value of median of \\{a_l, a_{l + 1}, …, a_r\}.
In this problem, for the integer multiset s, the median of s is equal to the ⌊ (|s|+1)/(2)⌋-th smallest number in it. For example, the median of \{1,4,4,6,5\} is 4, and the median of \{1,7,5,8\} is 5.
Slime wants Orac to make a_1 = a_2 = … = a_n = k using these operations.
Orac thinks that it is impossible, and he does not want to waste his time, so he decided to ask you if it is possible to satisfy the Slime's requirement, he may ask you these questions several times.
Input
The first line of the input is a single integer t: the number of queries.
The first line of each query contains two integers n\ (1≤ n≤ 100 000) and k\ (1≤ k≤ 10^9), the second line contains n positive integers a_1,a_2,...,a_n\ (1≤ a_i≤ 10^9)
The total sum of n is at most 100 000.
Output
The output should contain t lines. The i-th line should be equal to 'yes' if it is possible to make all integers k in some number of operations or 'no', otherwise. You can print each letter in lowercase or uppercase.
Example
Input
5
5 3
1 5 2 6 1
1 6
6
3 2
1 2 3
4 3
3 1 2 3
10 3
1 2 3 4 5 6 7 8 9 10
Output
no
yes
yes
no
yes
Note
In the first query, Orac can't turn all elements into 3.
In the second query, a_1=6 is already satisfied.
In the third query, Orac can select the complete array and turn all elements into 2.
In the fourth query, Orac can't turn all elements into 3.
In the fifth query, Orac can select [1,6] at first and then select [2,10].
Submitted Solution:
```
def case(A, k):
if A.count(k) == len(A):
print("yes")
return
N = len(A)
before_k = dict()
after_k = dict()
k_occured = False
bil = 0
for i in range(N):
if A[i] == k:
k_occured = True
before_k = { **before_k, **after_k }
else:
if A[i] > k:
bil += 1
else:
bil -= 1
if k_occured:
if i % 2 == 1:
if 1 in before_k.get(bil, set()):
print("yes")
return
if 0 in before_k.get(bil-1, set()):
print("yes")
return
else:
if 0 in before_k.get(bil, set()):
print("yes")
return
if 1 in before_k.get(bil-1, set()):
print("yes")
return
if bil in before_k:
before_k[bil].add(i % 2)
else:
before_k[bil] = { i % 2 }
k_occured = False
bil = 0
for i in range(N-1, -1, -1):
if A[i] == k:
k_occured = True
else:
if A[i] > k:
bil += 1
else:
bil -= 1
if bil == 0 and k_occured:
print("yes")
return
print("no")
t = int(input())
for i in range(t):
n, k = input().split(' ')
n, k = int(n), int(k)
A = list(map(int, input().split(' ')))
case(A, k)
``` | instruction | 0 | 53,250 | 5 | 106,500 |
No | output | 1 | 53,250 | 5 | 106,501 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of integers b_1, b_2, …, b_n.
An array a_1, a_2, …, a_n of integers is hybrid if for each i (1 ≤ i ≤ n) at least one of these conditions is true:
* b_i = a_i, or
* b_i = ∑_{j=1}^{i} a_j.
Find the number of hybrid arrays a_1, a_2, …, a_n. As the result can be very large, you should print the answer modulo 10^9 + 7.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line of each test case contains n integers b_1, b_2, …, b_n (-10^9 ≤ b_i ≤ 10^9).
It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, print a single integer: the number of hybrid arrays a_1, a_2, …, a_n modulo 10^9 + 7.
Example
Input
4
3
1 -1 1
4
1 2 3 4
10
2 -1 1 -2 2 3 -5 0 2 -1
4
0 0 0 1
Output
3
8
223
1
Note
In the first test case, the hybrid arrays are [1, -2, 1], [1, -2, 2], [1, -1, 1].
In the second test case, the hybrid arrays are [1, 1, 1, 1], [1, 1, 1, 4], [1, 1, 3, -1], [1, 1, 3, 4], [1, 2, 0, 1], [1, 2, 0, 4], [1, 2, 3, -2], [1, 2, 3, 4].
In the fourth test case, the only hybrid array is [0, 0, 0, 1].
Submitted Solution:
```
for s in[*open(0)][2::2]:
C=[0];D={0:1};S=1
for n in map(int,s.split()):C+=C[-1]+n,
for n in C[1:-1]:D[n],S=S,(2*S-D.get(n,0))%(10**9+7)
print(S)
``` | instruction | 0 | 53,311 | 5 | 106,622 |
Yes | output | 1 | 53,311 | 5 | 106,623 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of integers b_1, b_2, …, b_n.
An array a_1, a_2, …, a_n of integers is hybrid if for each i (1 ≤ i ≤ n) at least one of these conditions is true:
* b_i = a_i, or
* b_i = ∑_{j=1}^{i} a_j.
Find the number of hybrid arrays a_1, a_2, …, a_n. As the result can be very large, you should print the answer modulo 10^9 + 7.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line of each test case contains n integers b_1, b_2, …, b_n (-10^9 ≤ b_i ≤ 10^9).
It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, print a single integer: the number of hybrid arrays a_1, a_2, …, a_n modulo 10^9 + 7.
Example
Input
4
3
1 -1 1
4
1 2 3 4
10
2 -1 1 -2 2 3 -5 0 2 -1
4
0 0 0 1
Output
3
8
223
1
Note
In the first test case, the hybrid arrays are [1, -2, 1], [1, -2, 2], [1, -1, 1].
In the second test case, the hybrid arrays are [1, 1, 1, 1], [1, 1, 1, 4], [1, 1, 3, -1], [1, 1, 3, 4], [1, 2, 0, 1], [1, 2, 0, 4], [1, 2, 3, -2], [1, 2, 3, 4].
In the fourth test case, the only hybrid array is [0, 0, 0, 1].
Submitted Solution:
```
import sys
from sys import stdin
mod = 10**9+7
tt = int(stdin.readline())
for loop in range(tt):
n = int(stdin.readline())
b = [0] + list(map(int,stdin.readline().split()))
c = [0]
for i in range(1,n+1):
c.append( c[-1] + b[i] )
dic = {}
dic[0] = 1
ds = 1
for i in range(1,n+1):
nc = c[i-1]
if nc not in dic:
last = 0
else:
last = dic[nc]
dic[nc] = ds
ds -= last
ds += dic[nc]
ds %= mod
print (ds % mod)
``` | instruction | 0 | 53,314 | 5 | 106,628 |
Yes | output | 1 | 53,314 | 5 | 106,629 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of integers b_1, b_2, …, b_n.
An array a_1, a_2, …, a_n of integers is hybrid if for each i (1 ≤ i ≤ n) at least one of these conditions is true:
* b_i = a_i, or
* b_i = ∑_{j=1}^{i} a_j.
Find the number of hybrid arrays a_1, a_2, …, a_n. As the result can be very large, you should print the answer modulo 10^9 + 7.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line of each test case contains n integers b_1, b_2, …, b_n (-10^9 ≤ b_i ≤ 10^9).
It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, print a single integer: the number of hybrid arrays a_1, a_2, …, a_n modulo 10^9 + 7.
Example
Input
4
3
1 -1 1
4
1 2 3 4
10
2 -1 1 -2 2 3 -5 0 2 -1
4
0 0 0 1
Output
3
8
223
1
Note
In the first test case, the hybrid arrays are [1, -2, 1], [1, -2, 2], [1, -1, 1].
In the second test case, the hybrid arrays are [1, 1, 1, 1], [1, 1, 1, 4], [1, 1, 3, -1], [1, 1, 3, 4], [1, 2, 0, 1], [1, 2, 0, 4], [1, 2, 3, -2], [1, 2, 3, 4].
In the fourth test case, the only hybrid array is [0, 0, 0, 1].
Submitted Solution:
```
for s in[*open(0)][2::2]:
C=[0];N=0;D={};D[0]=S=1
for n in map(int,s.split()):C+=C[-1]+n,
for i in range(1,N):D[C[i]],S=S,(2*S-D.get(C[i],0))%(10**9+7)
print(S)
``` | instruction | 0 | 53,315 | 5 | 106,630 |
No | output | 1 | 53,315 | 5 | 106,631 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of integers b_1, b_2, …, b_n.
An array a_1, a_2, …, a_n of integers is hybrid if for each i (1 ≤ i ≤ n) at least one of these conditions is true:
* b_i = a_i, or
* b_i = ∑_{j=1}^{i} a_j.
Find the number of hybrid arrays a_1, a_2, …, a_n. As the result can be very large, you should print the answer modulo 10^9 + 7.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line of each test case contains n integers b_1, b_2, …, b_n (-10^9 ≤ b_i ≤ 10^9).
It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, print a single integer: the number of hybrid arrays a_1, a_2, …, a_n modulo 10^9 + 7.
Example
Input
4
3
1 -1 1
4
1 2 3 4
10
2 -1 1 -2 2 3 -5 0 2 -1
4
0 0 0 1
Output
3
8
223
1
Note
In the first test case, the hybrid arrays are [1, -2, 1], [1, -2, 2], [1, -1, 1].
In the second test case, the hybrid arrays are [1, 1, 1, 1], [1, 1, 1, 4], [1, 1, 3, -1], [1, 1, 3, 4], [1, 2, 0, 1], [1, 2, 0, 4], [1, 2, 3, -2], [1, 2, 3, 4].
In the fourth test case, the only hybrid array is [0, 0, 0, 1].
Submitted Solution:
```
import sys
input = sys.stdin.readline
mod = 10 ** 9 + 7
for _ in range(int(input())):
n = int(input())
B = list(map(int, input().split()))
dp = [0] * n
dp[0] = 1
if n == 1:
print(1)
else:
cur = B[0]
ans = 1
for i in range(1, n):
cur += B[i]
if B[i] != cur:
dp[i] = dp[i - 1] * 2 % mod
else:
dp[i] = dp[i - 1]
print(dp[-1])
``` | instruction | 0 | 53,316 | 5 | 106,632 |
No | output | 1 | 53,316 | 5 | 106,633 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of integers b_1, b_2, …, b_n.
An array a_1, a_2, …, a_n of integers is hybrid if for each i (1 ≤ i ≤ n) at least one of these conditions is true:
* b_i = a_i, or
* b_i = ∑_{j=1}^{i} a_j.
Find the number of hybrid arrays a_1, a_2, …, a_n. As the result can be very large, you should print the answer modulo 10^9 + 7.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line of each test case contains n integers b_1, b_2, …, b_n (-10^9 ≤ b_i ≤ 10^9).
It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, print a single integer: the number of hybrid arrays a_1, a_2, …, a_n modulo 10^9 + 7.
Example
Input
4
3
1 -1 1
4
1 2 3 4
10
2 -1 1 -2 2 3 -5 0 2 -1
4
0 0 0 1
Output
3
8
223
1
Note
In the first test case, the hybrid arrays are [1, -2, 1], [1, -2, 2], [1, -1, 1].
In the second test case, the hybrid arrays are [1, 1, 1, 1], [1, 1, 1, 4], [1, 1, 3, -1], [1, 1, 3, 4], [1, 2, 0, 1], [1, 2, 0, 4], [1, 2, 3, -2], [1, 2, 3, 4].
In the fourth test case, the only hybrid array is [0, 0, 0, 1].
Submitted Solution:
```
import sys
from sys import stdin
mod = 10**9+7
class SegTree:
def __init__(self,N,first):
self.NO = 2**(N-1).bit_length()
self.First = first
self.data = [first] * (2*self.NO)
def calc(self,l,r):
return (l+r) % mod
def update(self,ind,x):
ind += self.NO - 1
self.data[ind] = x
while ind >= 0:
ind = (ind - 1)//2
self.data[ind] = self.calc(self.data[2*ind+1],self.data[2*ind+2])
def query(self,l,r):
L = l + self.NO
R = r + self.NO
s = self.First
while L < R:
if R & 1:
R -= 1
s = self.calc(s , self.data[R-1])
if L & 1:
s = self.calc(s , self.data[L-1])
L += 1
L >>= 1
R >>= 1
return s
def get(self , ind):
ind += self.NO - 1
return self.data[ind]
tt = int(stdin.readline())
for loop in range(tt):
n = int(stdin.readline())
b = [0] + list(map(int,stdin.readline().split()))
c = [0]
for i in range(1,n+1):
c.append(c[-1] + b[i])
ctoi = {}
tlis = []
for i in range(len(c)):
if c[i] not in ctoi:
ctoi[c[i]] = 0
tlis.append(c[i])
tlis.sort()
for i in range(len(tlis)):
ctoi[tlis[i]] = i
ST = SegTree(len(tlis),0)
ST.update(0,1)
for i in range(1,n+1):
ind = ctoi[c[i-1]]
ST.update(ind , ST.query(0,len(tlis)))
print (ST.query(0,len(tlis)))
``` | instruction | 0 | 53,317 | 5 | 106,634 |
No | output | 1 | 53,317 | 5 | 106,635 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of integers b_1, b_2, …, b_n.
An array a_1, a_2, …, a_n of integers is hybrid if for each i (1 ≤ i ≤ n) at least one of these conditions is true:
* b_i = a_i, or
* b_i = ∑_{j=1}^{i} a_j.
Find the number of hybrid arrays a_1, a_2, …, a_n. As the result can be very large, you should print the answer modulo 10^9 + 7.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).
The second line of each test case contains n integers b_1, b_2, …, b_n (-10^9 ≤ b_i ≤ 10^9).
It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, print a single integer: the number of hybrid arrays a_1, a_2, …, a_n modulo 10^9 + 7.
Example
Input
4
3
1 -1 1
4
1 2 3 4
10
2 -1 1 -2 2 3 -5 0 2 -1
4
0 0 0 1
Output
3
8
223
1
Note
In the first test case, the hybrid arrays are [1, -2, 1], [1, -2, 2], [1, -1, 1].
In the second test case, the hybrid arrays are [1, 1, 1, 1], [1, 1, 1, 4], [1, 1, 3, -1], [1, 1, 3, 4], [1, 2, 0, 1], [1, 2, 0, 4], [1, 2, 3, -2], [1, 2, 3, 4].
In the fourth test case, the only hybrid array is [0, 0, 0, 1].
Submitted Solution:
```
for s in[*open(0)][2::2]:
C=[0];D={0:1};S=1
for n in map(int,s.split()):C+=C[-1]+n,;D[C[-1]]=0
for n in C[1:-1]:D[n],S=S,(2*S-D[n])%(10**9+7)
print(S)
``` | instruction | 0 | 53,318 | 5 | 106,636 |
No | output | 1 | 53,318 | 5 | 106,637 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Eugeny has array a = a1, a2, ..., an, consisting of n integers. Each integer ai equals to -1, or to 1. Also, he has m queries:
* Query number i is given as a pair of integers li, ri (1 ≤ li ≤ ri ≤ n).
* The response to the query will be integer 1, if the elements of array a can be rearranged so as the sum ali + ali + 1 + ... + ari = 0, otherwise the response to the query will be integer 0.
Help Eugeny, answer all his queries.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 2·105). The second line contains n integers a1, a2, ..., an (ai = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n).
Output
Print m integers — the responses to Eugene's queries in the order they occur in the input.
Examples
Input
2 3
1 -1
1 1
1 2
2 2
Output
0
1
0
Input
5 5
-1 1 1 1 -1
1 1
2 3
3 5
2 5
1 5
Output
0
1
0
1
0
Submitted Solution:
```
n,x=map(int,input().split())
a=list(map(int,input().split()))
d={1:0}
for i in a:
if i==1:
d[i]+=1
o=min(d[1],n-d[1])
k=[]
for i in range(x):
l,r=map(int,input().split())
k.append(int((l+r+1)&1==0 and o>=(r-l+1)//2))
print(*k)
``` | instruction | 0 | 53,387 | 5 | 106,774 |
Yes | output | 1 | 53,387 | 5 | 106,775 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Eugeny has array a = a1, a2, ..., an, consisting of n integers. Each integer ai equals to -1, or to 1. Also, he has m queries:
* Query number i is given as a pair of integers li, ri (1 ≤ li ≤ ri ≤ n).
* The response to the query will be integer 1, if the elements of array a can be rearranged so as the sum ali + ali + 1 + ... + ari = 0, otherwise the response to the query will be integer 0.
Help Eugeny, answer all his queries.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 2·105). The second line contains n integers a1, a2, ..., an (ai = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n).
Output
Print m integers — the responses to Eugene's queries in the order they occur in the input.
Examples
Input
2 3
1 -1
1 1
1 2
2 2
Output
0
1
0
Input
5 5
-1 1 1 1 -1
1 1
2 3
3 5
2 5
1 5
Output
0
1
0
1
0
Submitted Solution:
```
nm=input().split()
n=int(nm[0])
m=int(nm[1])
kol1=0
kolm1=0
v0and1=[]
a=input().split()
for i in range(n):
if a[i]=='1':
kol1+=1
continue
kolm1+=1
for i in range(m):
b=input().split()
b[0]=int(b[0])
b[1]=int(b[1])
if (b[1]-b[0]+1)%2==0 and (b[1]-b[0]+1)//2<=kol1 and (b[1]-b[0]+1)//2<=kolm1:
v0and1.append(1)
continue
v0and1.append(0)
for i in range(m):
print(v0and1[i])
``` | instruction | 0 | 53,388 | 5 | 106,776 |
Yes | output | 1 | 53,388 | 5 | 106,777 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Eugeny has array a = a1, a2, ..., an, consisting of n integers. Each integer ai equals to -1, or to 1. Also, he has m queries:
* Query number i is given as a pair of integers li, ri (1 ≤ li ≤ ri ≤ n).
* The response to the query will be integer 1, if the elements of array a can be rearranged so as the sum ali + ali + 1 + ... + ari = 0, otherwise the response to the query will be integer 0.
Help Eugeny, answer all his queries.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 2·105). The second line contains n integers a1, a2, ..., an (ai = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n).
Output
Print m integers — the responses to Eugene's queries in the order they occur in the input.
Examples
Input
2 3
1 -1
1 1
1 2
2 2
Output
0
1
0
Input
5 5
-1 1 1 1 -1
1 1
2 3
3 5
2 5
1 5
Output
0
1
0
1
0
Submitted Solution:
```
n , m = map(int,input().split())
arr = input().split()
x = arr.count('1')
y = n - x
ans = ''
for j in range(m):
l , r = map(int,input().split())
if (r - l + 1) % 2 == 0 and min(x , y) >= (r - l + 1)//2 :
ans += '1\n'
else:
ans += '0\n'
print(ans)
``` | instruction | 0 | 53,389 | 5 | 106,778 |
Yes | output | 1 | 53,389 | 5 | 106,779 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Eugeny has array a = a1, a2, ..., an, consisting of n integers. Each integer ai equals to -1, or to 1. Also, he has m queries:
* Query number i is given as a pair of integers li, ri (1 ≤ li ≤ ri ≤ n).
* The response to the query will be integer 1, if the elements of array a can be rearranged so as the sum ali + ali + 1 + ... + ari = 0, otherwise the response to the query will be integer 0.
Help Eugeny, answer all his queries.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 2·105). The second line contains n integers a1, a2, ..., an (ai = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n).
Output
Print m integers — the responses to Eugene's queries in the order they occur in the input.
Examples
Input
2 3
1 -1
1 1
1 2
2 2
Output
0
1
0
Input
5 5
-1 1 1 1 -1
1 1
2 3
3 5
2 5
1 5
Output
0
1
0
1
0
Submitted Solution:
```
a,q = map(int,input().split())
x = [int(x) for x in input().split()]
m = x.count(-1)
re = min(m,a-m)
ans = ''
for i in range(q):
l,r = map(int,input().split())
t = (r-l)+1
if (t%2==0)and(t//2<=re):
ans+='1\n'
else:
ans+='0\n'
print(ans)
``` | instruction | 0 | 53,390 | 5 | 106,780 |
Yes | output | 1 | 53,390 | 5 | 106,781 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Eugeny has array a = a1, a2, ..., an, consisting of n integers. Each integer ai equals to -1, or to 1. Also, he has m queries:
* Query number i is given as a pair of integers li, ri (1 ≤ li ≤ ri ≤ n).
* The response to the query will be integer 1, if the elements of array a can be rearranged so as the sum ali + ali + 1 + ... + ari = 0, otherwise the response to the query will be integer 0.
Help Eugeny, answer all his queries.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 2·105). The second line contains n integers a1, a2, ..., an (ai = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n).
Output
Print m integers — the responses to Eugene's queries in the order they occur in the input.
Examples
Input
2 3
1 -1
1 1
1 2
2 2
Output
0
1
0
Input
5 5
-1 1 1 1 -1
1 1
2 3
3 5
2 5
1 5
Output
0
1
0
1
0
Submitted Solution:
```
col, lin = [int(item) for item in input().split()]
lista = list(input()) # lista de str
neg = 0
pos = 0
for i in range(col):
if lista[i] == "-1":
neg += 1
else:
pos += 1
for j in range(lin):
a, b = [int(item) for item in input().split()]
intervalo = a - b + 1
if intervalo % 2 == 0 and intervalo//2 <= pos and intervalo//2 <= neg:
print(1)
else:
print(0)
``` | instruction | 0 | 53,391 | 5 | 106,782 |
No | output | 1 | 53,391 | 5 | 106,783 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Eugeny has array a = a1, a2, ..., an, consisting of n integers. Each integer ai equals to -1, or to 1. Also, he has m queries:
* Query number i is given as a pair of integers li, ri (1 ≤ li ≤ ri ≤ n).
* The response to the query will be integer 1, if the elements of array a can be rearranged so as the sum ali + ali + 1 + ... + ari = 0, otherwise the response to the query will be integer 0.
Help Eugeny, answer all his queries.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 2·105). The second line contains n integers a1, a2, ..., an (ai = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n).
Output
Print m integers — the responses to Eugene's queries in the order they occur in the input.
Examples
Input
2 3
1 -1
1 1
1 2
2 2
Output
0
1
0
Input
5 5
-1 1 1 1 -1
1 1
2 3
3 5
2 5
1 5
Output
0
1
0
1
0
Submitted Solution:
```
n, m = map(int, input().split())
a = list(map(int, input().split()))
a1 = a.count(1)
a11 = a.count(-1)
for i in range(m):
l, r = map(int, input().split())
k = l-r+1
if k % 2 == 0 and a1 >= k/2 and a11 >= k/2: print(1)
else: print(0)
``` | instruction | 0 | 53,393 | 5 | 106,786 |
No | output | 1 | 53,393 | 5 | 106,787 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Eugeny has array a = a1, a2, ..., an, consisting of n integers. Each integer ai equals to -1, or to 1. Also, he has m queries:
* Query number i is given as a pair of integers li, ri (1 ≤ li ≤ ri ≤ n).
* The response to the query will be integer 1, if the elements of array a can be rearranged so as the sum ali + ali + 1 + ... + ari = 0, otherwise the response to the query will be integer 0.
Help Eugeny, answer all his queries.
Input
The first line contains integers n and m (1 ≤ n, m ≤ 2·105). The second line contains n integers a1, a2, ..., an (ai = -1, 1). Next m lines contain Eugene's queries. The i-th line contains integers li, ri (1 ≤ li ≤ ri ≤ n).
Output
Print m integers — the responses to Eugene's queries in the order they occur in the input.
Examples
Input
2 3
1 -1
1 1
1 2
2 2
Output
0
1
0
Input
5 5
-1 1 1 1 -1
1 1
2 3
3 5
2 5
1 5
Output
0
1
0
1
0
Submitted Solution:
```
n,m=map(int,input().split())
arr=list(map(int,input().split()))
p=0
for i in arr:
if i==1:
p+=1
ne=p-n
for i in range(m):
a,b=map(int,input().split())
a-=1
if (b-a)%2==1 or a==b:
print(0)
else:
if ne>=int((b-a)/2) and p>=int((b-a)/2):
print(1)
else:
print(0)
# n,m=map(int,input().split())
# arr=list(map(int,input().split()))
# for i in range(m):
# a,b=map(int,input().split())
# s=0
# if a==b:
# print(0)
# else:
# for j in range(a-1,b):
# # print(j)
# s+=arr[j]
# # print(i,s,arr)
# if s==0:
# print(1)
# else:
# print(0)
``` | instruction | 0 | 53,394 | 5 | 106,788 |
No | output | 1 | 53,394 | 5 | 106,789 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61 | instruction | 0 | 53,438 | 5 | 106,876 |
Tags: dp, implementation
Correct Solution:
```
n,m,k=map(int,input().split())
p=list(map(int,input().split()))
if m==1:
print(sum(sorted(p)[-k:]))
exit()
s=sum(p[:m])
i,j=0,m
l=[s]
while j<n:
s=s-p[i]+p[j]
i+=1;j+=1
l.append(s)
n=len(l)
dp=[[0]*(n+1) for i in range(k+1)]
for i in range(1,n+1):
dp[1][i]=max(dp[1][i-1],l[i-1])
for i in range(2,k+1):
for j in range(m*(i-1)+1,n+1):
dp[i][j]=max(dp[i][j-1],dp[i-1][j-m]+l[j-1])
print(dp[-1][-1])
``` | output | 1 | 53,438 | 5 | 106,877 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61 | instruction | 0 | 53,439 | 5 | 106,878 |
Tags: dp, implementation
Correct Solution:
```
n, m, k = list(map(int, input().split()))
a = list(map(int, input().split()))
p_a = [0 for _ in range(n)]
p_a[0] = a[0]
for i in range(1, n):
p_a[i] = p_a[i - 1] + a[i]
INF = -1e10
# print(p_a)
dp = {}
from types import GeneratorType
def bootstrap(f, stack=[]):
def wrappedfunc(*args, **kwargs):
if stack:
return f(*args, **kwargs)
else:
to = f(*args, **kwargs)
while True:
if type(to) is GeneratorType:
stack.append(to)
to = next(to)
else:
stack.pop()
if not stack:
break
to = stack[-1].send(to)
return to
return wrappedfunc
@bootstrap
def solve(i, k, m):
if (i, k, m) in dp:
yield dp[(i, k, m)]
if k == 0:
dp[(i, k, m)] = 0
yield 0
if i + m == n:
if k == 1:
# print(p_a[n - 1] - p_a[i - 1])
if i==0:
dp[(i, k, m)]=p_a[n - 1]
else:
dp[(i, k, m)] = p_a[n - 1] - p_a[i - 1]
yield dp[(i, k, m)]
if k > 1:
dp[(i, k, m)] = INF
yield INF
if i + m > n - 1:
dp[(i, k, m)] = INF
yield INF
if k == 0:
dp[(i, k, m)] = 0
yield 0
if i == 0:
a=yield solve(i + 1, k, m)
b=yield solve(i + m, k - 1, m)
dp[(i, k, m)] = max(a ,b+ p_a[i + m - 1])
yield dp[(i, k, m)]
else:
a = yield solve(i + 1, k, m)
b=yield solve(i + m, k - 1, m)
dp[(i, k, m)] = max(a, b+ p_a[i + m - 1] - p_a[i - 1])
yield dp[(i, k, m)]
if m==1:print(sum(sorted(a)[n-k:]))
else:
print(solve(0, k, m))
``` | output | 1 | 53,439 | 5 | 106,879 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61 | instruction | 0 | 53,440 | 5 | 106,880 |
Tags: dp, implementation
Correct Solution:
```
n, m, k = map(int, input().split())
lst = list(map(int, input().split()))
if m == 1:
print(sum(sorted(lst)[-k:]))
exit()
s = sum(lst[:m])
i, j = 0, m
l = [s]
while j < n:
s = s - lst[i] + lst[j]
i +=1
j += 1
l.append(s)
n = len(l)
dp = [[0] * (n+1) for i in range(k+1)]
for i in range(1, n+1):
dp[1][i] = max(dp[1][i-1], l[i-1])
for i in range(2, k+1):
for j in range(m*(i-1)+1, n+1):
dp[i][j] = max(dp[i][j-1], dp[i-1][j-m]+l[j-1])
print(dp[-1][-1])
``` | output | 1 | 53,440 | 5 | 106,881 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61 | instruction | 0 | 53,441 | 5 | 106,882 |
Tags: dp, implementation
Correct Solution:
```
n,m,k = map(int,input().split())
arr = list(map(int,input().split()))
for i in range(1,n):
arr[i]+= arr[i-1]
for i in range(n-1,m-1,-1):
arr[i]-= arr[i-m]
dp = [0]*n
for ink in range(1,k+1):
ndp = [0]*n
for i in range(ink*m-1,n-(k-ink)*m):
ndp[i] = max(dp[i-m]+ arr[i],ndp[i-1])
dp = ndp[:]
print(dp[n-1])
``` | output | 1 | 53,441 | 5 | 106,883 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61 | instruction | 0 | 53,442 | 5 | 106,884 |
Tags: dp, implementation
Correct Solution:
```
n,m,k = map(int,input().split())
l = list(map(int,input().split()))
if(m==1):
l.sort()
ans = 0
for i in range(k):
ans+=l[n-1-i]
print(ans)
exit()
pres =[]
s=0
pres.append(0)
for i in l:
s+=i
pres.append(s)
dp = [[0 for i in range(n+1)]for j in range(k+1)]
for i in range(k+1):
for j in range(n+1):
if(i==0):
dp[i][j]=0
elif(j<i*m):
dp[i][j]=0
elif(j==i*m):
dp[i][j] = pres[j]
else:
dp[i][j] = max(dp[i][j-1],pres[j]- pres[j-m] + dp[i-1][j-m])
print(dp[k][n])
``` | output | 1 | 53,442 | 5 | 106,885 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61 | instruction | 0 | 53,443 | 5 | 106,886 |
Tags: dp, implementation
Correct Solution:
```
import sys, math
input = sys.stdin.readline
def getInts():
return [int(s) for s in input().split()]
def getInt():
return int(input())
def getStrs():
return [s for s in input().split()]
def getStr():
return input().strip()
def listStr():
return list(input().strip())
import collections as col
import math
def solve():
N, M, K = getInts()
P = getInts()
#suppose we have already chosen i blocks of m, and the last used index was j
#deal with worst case in order N log N time
if M == 1:
P.sort(reverse=True)
return sum(P[:K])
PP = [0]
curr_sum = 0
for p in P:
curr_sum += p
PP.append(curr_sum)
dp = [[0 for j in range(N+1)] for i in range(K+1)]
#dp[0][j] = 0 for all j
#dp[i][0] = 0 for all i
#Consider dp[1][0] (suppose M==1)
#dp[1][1] = min(dp[0][1],dp[0][0]+PP[1]-PP[0])
for i in range(1,K+1):
#j is the number of elements used, i.e. up to index j-1 since it is 0-based
for j in range(1,N+1):
if i*M > j:
continue
dp[i][j] = max(dp[i][j-1],dp[i-1][j-M]+PP[j]-PP[j-M])
#print(dp)
return dp[K][N]
print(solve())
``` | output | 1 | 53,443 | 5 | 106,887 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61 | instruction | 0 | 53,444 | 5 | 106,888 |
Tags: dp, implementation
Correct Solution:
```
from sys import stdin, setrecursionlimit
from collections import *
import threading
def arr_inp(n):
if n == 1:
return [int(x) for x in stdin.readline().split()]
elif n == 2:
return [float(x) for x in stdin.readline().split()]
else:
return list(stdin.readline()[:-1])
def dp(i, num):
if num > k:
return -float('inf')
if i >= n - m + 1:
return 0
if mem[i, num] != -1:
return mem[i, num]
mem[i, num] = max(dp(i + 1, num), cum[i] + dp(i + m, num + 1))
return mem[i, num]
def main():
ans = 0
if m == 1:
print(sum(sorted(a)[n - k:]))
else:
for i in range(n - m + 1):
ans = max(ans, dp(i, 0))
print(ans)
if __name__ == '__main__':
n, m, k = arr_inp(1)
a = arr_inp(1)
mem, cum = defaultdict(lambda: -1), [sum(a[i:i + m]) for i in range(n - m + 1)]
setrecursionlimit(50000)
threading.stack_size(102400000)
thread = threading.Thread(target=main)
thread.start()
``` | output | 1 | 53,444 | 5 | 106,889 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61 | instruction | 0 | 53,445 | 5 | 106,890 |
Tags: dp, implementation
Correct Solution:
```
import sys
def solve(n, m, k, a):
# s = set(a)
if m == 1:
if k == n:
return sum(a)
else:
return sum(sorted(a, reverse=True)[:k])
r0 = m + 0 - 1
sum0 = sum(a[:r0 + 1])
s = [sum0]
for i in range(r0 + 1, n):
sum0 = sum0 + a[i] - a[i - m]
s.append(sum0)
t = [0] * len(s)
# t = [[0] * len(s) for _ in range(k)]
# nt = [0] * len(s)
t[0] = s[0]
for i in range(1, len(s)):
t[i] = max(s[i], t[i - 1])
for i in range(1, k):
nt = [0] * len(s)
for j in range(i * m, len(s)):
nt[j] = t[j - m] + s[j]
nt[j] = max(nt[j], nt[j - 1])
t = nt
return t[-1]
# assert solve(5, 2, 1, list(map(int, '1 2 3 4 5'.split()))) == 9
# assert solve(7, 1, 3, list(map(int, '2 10 7 18 5 33 0'.split()))) == 61
n, m, k = map(int, sys.stdin.readline().strip().split())
numbers = list(map(int, sys.stdin.readline().strip().split()))
r = solve(n, m, k, numbers)
print(r)
``` | output | 1 | 53,445 | 5 | 106,891 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61
Submitted Solution:
```
n, m, k = map(int, input().split())
p = list(map(int, input().split()))
if m == 1:
p.sort()
print(sum(p[n-k:n]))
else:
curr_s2 = [0] + p
for i in range(1, n + 1):
curr_s2[i] += curr_s2[i - 1]
d = [[0 for i in range(n + 1)] for j in range(k + 1)]
for i in range(1, k + 1):
for j in range(i * m, n + 1):
d[i][j] = max(d[i][j - 1], d[i - 1][j - m] + curr_s2[j] - curr_s2[j - m])
#print(d)
print(d[k][n])
``` | instruction | 0 | 53,446 | 5 | 106,892 |
Yes | output | 1 | 53,446 | 5 | 106,893 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61
Submitted Solution:
```
import math
def func(i,k):
global prefix
global m
global dp
# print('i',i,'k',k,m)
for i in range(n):
for j in range(k+1):
if(j==0 or i<m-1):
dp[i][j]=0
elif(i==m-1):
if(j==1):
dp[i][j]=prefix[i]
else:
dp[i][j]=-math.inf
else:
dp[i][j]=max(dp[i-1][j],prefix[i]-prefix[i-m]+dp[i-m][j-1])
return dp[n-1][k]
n,m,k=tuple(map(int,input().split()))
a=list(map(int,input().split()))
#a=list(map(int,input().split()))*100
#n=len(a)
#print(n)
#m,k=77,15
prefix=[0]*n
for i in range(n):
if(i==0):
prefix[i]=a[i]
else:
prefix[i]=prefix[i-1]+a[i]
# print(prefix)
dp=[[-1 for i in range(k+1)] for j in range(n)]
if(m*k==n):
print(sum(a))
else:
print(func(n-1,k))
# print(sum(sorted(a)[::-1][:m*k]))
``` | instruction | 0 | 53,447 | 5 | 106,894 |
Yes | output | 1 | 53,447 | 5 | 106,895 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61
Submitted Solution:
```
inp = lambda: map(int, input().rstrip().split())
n, m, k = inp()
p = list(inp())
if m == 1:
p.sort(reverse=True)
print(sum(p[:k]))
exit()
a = [[0] * (k + 1) for i in range(n + 1)]
b = [0]
for i in range(n):
b.append(b[-1] + p[i])
for i in range(1, n + 1):
for j in range(1, k + 1):
if j * m > i:
break
a[i][j] = max(a[max(0, i - 1)][j], a[max(0, i - m)][j - 1] + b[i] - b[i - m])
print(a[n][k])
``` | instruction | 0 | 53,448 | 5 | 106,896 |
Yes | output | 1 | 53,448 | 5 | 106,897 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61
Submitted Solution:
```
#pyrival orz
import os
import sys
from io import BytesIO, IOBase
input = sys.stdin.readline
############ ---- Input Functions ---- ############
def inp():
return(int(input()))
def inlt():
return(list(map(int,input().split())))
def insr():
s = input()
return(list(s[:len(s) - 1]))
def invr():
return(map(int,input().split()))
def main():
try:
n, m, k = invr()
a = inlt()
if m == 1:
print(sum(sorted(a, reverse=True)[:k]))
return True
pre, x = [0], 0
for i in range(n):
x += a[i]
pre.append(x)
dp = [[0]*(n+1) for i in range(k+1)]
for i in range(1, k+1):
for j in range(i*m, n+1):
dp[i][j] = max(dp[i][j-1], pre[j] - pre[j-m] + dp[i-1][j-m])
print(dp[k][n])
except Exception as e:
print(e)
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# endregion
if __name__ == "__main__":
main()
``` | instruction | 0 | 53,449 | 5 | 106,898 |
Yes | output | 1 | 53,449 | 5 | 106,899 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61
Submitted Solution:
```
n,m,k=map(int,input().split())
p=list(map(int,input().split()))
INF=10**18
r=n-m*k
if r==0:
print(sum(p))
exit()
dp=[[INF]*(r+1) for i in range(n)]
dp[0][1]=p[0]
for i in range(n):
dp[i][0]=0
for i in range(1,n):
for j in range(1,r+1):
if i<=m:
dp[i][j]=min(dp[i-1][j],dp[i-1][j-1]+p[i])
else:
dp[i][j]=min(dp[i-1][j],dp[i-1][j-1]+p[i],dp[i-1-m][j-1]+p[i])
print(sum(p)-dp[n-1][r])
``` | instruction | 0 | 53,450 | 5 | 106,900 |
No | output | 1 | 53,450 | 5 | 106,901 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61
Submitted Solution:
```
#=================================
# Author: Danish Amin
# Date: Sat Nov 14 14:45:17 2020
#=================================
# from debug import *
import sys; input = sys.stdin.readline
n, m , k = map(int, input().split())
lis = list(map(int, input().split()))
p = n-m*k
inf = int(1e10)
dp = [[-1]*(p+1) for i in range(n)]
def sol(i, j):
if j<=0: return 0
if i>=n: return inf
if dp[i][j] != -1: return dp[i][j]
ans = sol(i+1, j-1)
for v in range(i+m+1, n): ans = min(ans, sol(v, j-1))
dp[i][j] = lis[i]+ans
return dp[i][j]
sol(0, p)
v = inf
for i in range(n):
v = min(v, sol(i, p))
print(sum(lis) - v)
``` | instruction | 0 | 53,451 | 5 | 106,902 |
No | output | 1 | 53,451 | 5 | 106,903 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61
Submitted Solution:
```
n, m, k = map(int, input().split())
arr = list(map(int, input().split()))
pairs = []
for i in range(n-m):
pairs.append((i, sum(arr[i:i+m])))
pairs = sorted(pairs, reverse=True, key=lambda t: t[1])
s = 0
for i in range(k):
s += pairs[i*m][1]
print(s)
``` | instruction | 0 | 53,452 | 5 | 106,904 |
No | output | 1 | 53,452 | 5 | 106,905 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.
Given a sequence of n integers p1, p2, ..., pn. You are to choose k pairs of integers:
[l1, r1], [l2, r2], ..., [lk, rk] (1 ≤ l1 ≤ r1 < l2 ≤ r2 < ... < lk ≤ rk ≤ n; ri - li + 1 = m),
in such a way that the value of sum <image> is maximal possible. Help George to cope with the task.
Input
The first line contains three integers n, m and k (1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ 109).
Output
Print an integer in a single line — the maximum possible value of sum.
Examples
Input
5 2 1
1 2 3 4 5
Output
9
Input
7 1 3
2 10 7 18 5 33 0
Output
61
Submitted Solution:
```
n, m, k = map(int, input().split())
p = list(map(int, input().split()))
s = [0 for i in range(n - m + 1)]
curr_s2 = [0] + p
#curr_s2[0] = p[0]
for i in range(1, n + 1):
curr_s2[i] += curr_s2[i - 1]
d = [[0 for i in range(n)] for j in range(k)]
#d[1][0] = 1
#d[0][1] = 2
#print(d)
d[0][m - 1] = s[0]
for j in range(m, n):
d[0][j] = max(d[0][j - 1], s[j - m + 1])
#print(d)
for i in range(2, k + 1):
for j in range(i * m - 1, n):
d[i - 1][j] = max(d[i - 1][j - 1], d[i - 2][j - m] + curr_s2[j + 1] - curr_s2[j - m + 1])
#print(d)
print(d[k - 1][n - 1])
``` | instruction | 0 | 53,453 | 5 | 106,906 |
No | output | 1 | 53,453 | 5 | 106,907 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8 | instruction | 0 | 53,655 | 5 | 107,310 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
import sys
from collections import Counter
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
N = int(readline())
cnt = Counter()
for i in range(N):
cnt_2 = 0
cnt_5 = 0
a = float(readline())
a = int(a * (10**9)+0.5)
while a % 2 == 0:
a //= 2
cnt_2 += 1
while a % 5 == 0:
a //= 5
cnt_5 += 1
cnt[(cnt_2-9,cnt_5-9)] += 1
ans = 0
for (x1,y1),c1 in cnt.items():
for (x2,y2),c2 in cnt.items():
if x1+x2 >= 0 and y1+y2 >= 0:
if x1 == x2 and y1 == y2:
ans += c1*(c1-1)
else:
ans += c1*c2
print(ans//2)
``` | output | 1 | 53,655 | 5 | 107,311 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8 | instruction | 0 | 53,656 | 5 | 107,312 |
"Correct Solution:
```
n=int(input())
dp=[[0]*19 for _ in range(19)]
ans=0
for _ in range(n):
a=round(float(input())*10**9)
f,t=0,0
while a%2==0:
t+=1
a//=2
while a%5==0:
f+=1
a//=5
t,f=min(t,18),min(f,18)
ans+=dp[18-t][18-f]
for i in range(t+1):
for j in range(f+1):
dp[i][j]+=1
print(ans)
``` | output | 1 | 53,656 | 5 | 107,313 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8 | instruction | 0 | 53,657 | 5 | 107,314 |
"Correct Solution:
```
N = int(input())
A = {}
# 2, 5 , sum has to be >= 18 for both
for _ in range(N):
a = round(float(input())*10**9)
#print(a)
pow2 = 0
pow5 = 0
while a % 2 == 0 and pow2 < 18:
pow2 += 1
a //= 2
while a % 5 ==0 and pow5 < 18:
pow5 += 1
a //= 5
if (pow2, pow5) not in A:
A[(pow2, pow5)] = 0
A[(pow2, pow5)] += 1
#print(a, pow2, pow5)
#print(A)
ans = 0
for p1, c1 in A.items():
for p2, c2 in A.items():
if p1[0] + p2[0] < 18 or p1[1] + p2[1] < 18:
continue
if p1 == p2:
ans += c1 * (c1 - 1)
else:
ans += c1 * c2
print(ans // 2)
``` | output | 1 | 53,657 | 5 | 107,315 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8 | instruction | 0 | 53,658 | 5 | 107,316 |
"Correct Solution:
```
from fractions import Fraction
from decimal import Decimal
n=int(input())
a=[Fraction(Decimal(input())) for _ in range(n)]
num=[aa.numerator*10**9//aa.denominator for aa in a]
cnt=[[0]*50 for _ in range(50)]
pair=[]
for nu in num:
c2=0
c5=0
while nu>0 and nu%2==0:
nu//=2
c2+=1
while nu>0 and nu%5==0:
nu//=5
c5+=1
cnt[c2][c5]+=1
pair.append((c2,c5))
ans=0
for i in range(49,-1,-1):
for j in range(49,-1,-1):
if i+1<49:
cnt[i][j]+=cnt[i+1][j]
if j+1<49:
cnt[i][j]+=cnt[i][j+1]
if i+1<49 and j+1<49:
cnt[i][j]-=cnt[i+1][j+1]
for c2,c5 in pair:
ans+=cnt[max(0,18-c2)][max(0,18-c5)]
if c2>=9 and c5>=9:
ans-=1
print(ans//2)
``` | output | 1 | 53,658 | 5 | 107,317 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8 | instruction | 0 | 53,659 | 5 | 107,318 |
"Correct Solution:
```
# A
from decimal import *
n = int(input())
a_l = [int(Decimal(input()) * 10**9) for x in range(n)]
list = [[0] * 19 for _ in range(19)]
cs_list = [[0] * 19 for _ in range(19)]
b_l = [0, 0] * n
for i in range(n):
_t2 = 0
_t5 = 0
_a = a_l[i]
while _a % 2 == 0 and _t2 < 18:
_t2 += 1
_a /= 2
_a = a_l[i]
while _a % 5 == 0 and _t5 < 18:
_t5 += 1
_a /= 5
list[_t2][_t5] += 1
b_l[i] = [_t2, _t5]
for i in range(19):
for j in range(19):
for k in range(i+1):
for l in range(j+1):
cs_list[k][l] += list[i][j]
ans = 0
for i in range(n):
_t,_f = b_l[i]
if _t >= 9 and _f >= 9:
ans -= 1
ans += cs_list[18-_t][18-_f]
print(ans // 2)
``` | output | 1 | 53,659 | 5 | 107,319 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8 | instruction | 0 | 53,660 | 5 | 107,320 |
"Correct Solution:
```
from collections import defaultdict
N = int(input())
twofive = defaultdict(int)
for i in range(N):
a = round(float(input()) * (10**9))
b = 0
c = 0
while a % 2 == 0 and b < 18:
b += 1
a //= 2
while a % 5 == 0 and c < 18:
c += 1
a //= 5
twofive[(b, c)] += 1
ans = 0
for b, c in twofive.keys():
for d, e in twofive.keys():
if b + d >= 18 and c + e >= 18:
if (b, c) != (d, e):
ans += twofive[(b, c)] * twofive[(d, e)]
else:
ans += twofive[(b, c)] * (twofive[(b, c)] - 1)
print(ans//2)
``` | output | 1 | 53,660 | 5 | 107,321 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8 | instruction | 0 | 53,661 | 5 | 107,322 |
"Correct Solution:
```
N = int(input())
p2 = [0] * N
p5 = [0] * N
out = 0
for i in range(N):
s = input()
if '.' in s:
a, b = s.split('.')
inp = int(a+b)
twos = -len(b)
fives = -len(b)
else:
inp = int(s)
twos = 0
fives = 0
while inp % 2 == 0:
twos += 1
inp //= 2
while inp % 5 == 0:
fives += 1
inp //= 5
if twos >= 0 and fives >= 0:
out -= 1
p2[i] = twos
p5[i] = fives
count = [[0] * 105 for i in range(105)]
for i in range(N):
count[p2[i]][p5[i]] += 1
pref = [[0] * 105 for i in range(105)]
for i in range(50,-51,-1):
for j in range(50, -51, -1):
curr = count[i][j]
curr += pref[i + 1][j]
curr += pref[i][j + 1]
curr -= pref[i + 1][j + 1]
pref[i][j] = curr
for i in range(N):
out += pref[-p2[i]][-p5[i]]
#print(pref[-p2[i]][-p5[i]])
print(out//2)
``` | output | 1 | 53,661 | 5 | 107,323 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8 | instruction | 0 | 53,662 | 5 | 107,324 |
"Correct Solution:
```
from decimal import Decimal
N, *A = map(Decimal, open(0).read().split())
N = int(N)
d = {}
for a in A:
a = int(a * (10 ** 9))
if a == 0:
t = (0, 0)
else:
x = -9
while a % 2 == 0:
x += 1
a //= 2
y = -9
while a % 5 == 0:
y += 1
a //= 5
t = (x, y)
d.setdefault(t, 0)
d[t] += 1
result = 0
xs = list(d.keys())
for i in range(len(xs)):
x, y = xs[i]
t = d[xs[i]]
if x >= 0 and y >= 0:
result += t * (t - 1) // 2
for j in range(i + 1, len(xs)):
m, n = xs[j]
if x + m >= 0 and y + n >= 0:
result += t * d[xs[j]]
print(result)
``` | output | 1 | 53,662 | 5 | 107,325 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8
Submitted Solution:
```
import sys
readline = sys.stdin.readline
N = int(readline())
C = [[0] * 19 for i in range(19)]
for i in range(N):
a = readline().rstrip()
if "." in a:
keta = len(a.split(".")[1])
a = int(a.replace(".","")) * (10 ** (9 - keta))
else:
a = int(a) * (10 ** 9)
cnt2 = 0
cnt5 = 0
while a % 2 == 0:
a //= 2
cnt2 += 1
while a % 5 == 0:
a //= 5
cnt5 += 1
C[min(cnt2, 18)][min(cnt5, 18)] += 1
#for c in C:
# print(c)
ans = 0
# まず、同じグループから2つの数を選ぶ場合の数
for i in range(9, 19):
for j in range(9, 19):
n = C[i][j]
ans += (n * (n - 1)) // 2
# 異なるグループから選ぶ場合の数
ans_diff = 0
for i in range(19):
for j in range(19):
for p in range(19):
for q in range(19):
if i == p and j == q:
continue # カウント済
if i + p < 18 or j + q < 18:
continue
ans_diff += C[i][j] * C[p][q]
ans += ans_diff // 2 # 二回カウントしている
print(ans)
``` | instruction | 0 | 53,663 | 5 | 107,326 |
Yes | output | 1 | 53,663 | 5 | 107,327 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8
Submitted Solution:
```
import sys
input = sys.stdin.readline
n = int(input())
ans = 0
cnt = [[0]*20 for _ in range(45)]
for _ in range(n):
a = list(map(str, input().rstrip().split(".")))
x = 0
if len(a) == 1:
x = int(a[0]) * 10**9
else:
x = int(a[0]) * 10**9 + int(a[1]) * pow(10, 9-len(a[1]))
cnt_2, cnt_5 = 0, 0
while x % 2 == 0:
cnt_2 += 1
x //= 2
while x % 5 == 0:
cnt_5 += 1
x //= 5
for i in range(45):
for j in range(20):
if cnt_2 + i >= 18 and cnt_5 + j >= 18:
ans += cnt[i][j]
cnt[cnt_2][cnt_5] += 1
print(ans)
``` | instruction | 0 | 53,664 | 5 | 107,328 |
Yes | output | 1 | 53,664 | 5 | 107,329 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.
Constraints
* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.
Input
Input is given from Standard Input in the following format.
N
A_1
A_2
\vdots
A_N
Output
Print the number of pairs with integer product A_i \cdot A_j (and i < j).
Examples
Input
5
7.5
2.4
17.000000001
17
16.000000000
Output
3
Input
11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001
Output
8
Submitted Solution:
```
n=int(input())
a=[input() for _ in range(n)]
m=30
c=[[0]*m for _ in range(m)]
k=9
ary=[]
for b in a:
b=b.split('.')
bint,bfl=0,0
bint=int(b[0])*10**9
if len(b)>1:
tmp=('1'+b[1]+'000000000000')[:10]
bfl=int(tmp)
bfl-=10**9
tmp=bint+bfl
t=tmp
n5=0
while t%5==0:
t//=5
n5+=1
t=tmp
n2=0
while t%2==0:
t//=2
n2+=1
n2=min(n2,k+9)
n5=min(n5,k+9)
c[n2][n5]+=1
ary.append([n2,n5])
cc=[[0]*(m+1) for _ in range(m+1)]
for i in range(m):
for j in range(m):
cc[i+1][j+1]+=cc[i+1][j]+c[i][j]
for i in range(m):
for j in range(m):
cc[i+1][j+1]+=cc[i][j+1]
ans=0
for i,j in ary:
if i>=k and j>=k:ans-=1
tmp=cc[-1][-1]-cc[-1][2*k-j]-cc[2*k-i][-1]+cc[2*k-i][2*k-j]
ans+=tmp
ans//=2
print(ans)
"""
c[k][k]+=7
for x in c:
print(x)
print('======')
for x in cc:
print(x)
"""
``` | instruction | 0 | 53,665 | 5 | 107,330 |
Yes | output | 1 | 53,665 | 5 | 107,331 |
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