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 |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961 | instruction | 0 | 90,783 | 5 | 181,566 |
"Correct Solution:
```
x=int(input())
nums=[1]
for b in range(2,x):
p=2
while b**p<=x:
nums.append(b**p)
p+=1
print(max(nums))
``` | output | 1 | 90,783 | 5 | 181,567 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961 | instruction | 0 | 90,784 | 5 | 181,568 |
"Correct Solution:
```
X = int(input())
ans = 1
i = 2
while i * i <= X:
a = i
while a * i <= X:
a *= i
ans = max(ans, a)
i += 1
print(ans)
``` | output | 1 | 90,784 | 5 | 181,569 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961 | instruction | 0 | 90,785 | 5 | 181,570 |
"Correct Solution:
```
x=int(input())
ans=0
for i in range(33):
for j in range(2,10):
if i**j<=x:
ans=max(ans,i**j)
print(ans)
``` | output | 1 | 90,785 | 5 | 181,571 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961
Submitted Solution:
```
x=int(input())
while sum(round(x**(1/k))**k!=x for k in [2,3,5,7])==4:
x-=1
print(x)
``` | instruction | 0 | 90,786 | 5 | 181,572 |
Yes | output | 1 | 90,786 | 5 | 181,573 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961
Submitted Solution:
```
X = int(input())
c = {i ** j for i in range(34) for j in range(2, 11) if i ** j <= 1000}
print(max([i for i in c if i <= X]))
``` | instruction | 0 | 90,787 | 5 | 181,574 |
Yes | output | 1 | 90,787 | 5 | 181,575 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961
Submitted Solution:
```
x=int(input())
ans=1
for a in range(2,1000):
p=2
while a**p<=x:
ans=max(ans,a**p)
p+=1
print(ans)
``` | instruction | 0 | 90,788 | 5 | 181,576 |
Yes | output | 1 | 90,788 | 5 | 181,577 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961
Submitted Solution:
```
X=int(input())
res=1
for b in range(2,1000):
for p in range(2,10):
if b**p<=X:
res=max(res,b**p)
print(res)
``` | instruction | 0 | 90,789 | 5 | 181,578 |
Yes | output | 1 | 90,789 | 5 | 181,579 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961
Submitted Solution:
```
x=int(input())
a=[1]
for i in range(2,32):
for j in range(1,32):
if i**j<=x:
a.append(i**j)
print(max(a))
``` | instruction | 0 | 90,790 | 5 | 181,580 |
No | output | 1 | 90,790 | 5 | 181,581 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961
Submitted Solution:
```
X=int(input())
max=1
for j in range(2,X):
for i in range(1,X):
if i**j<=X and i**j>max:
max=i**j
print(max)
``` | instruction | 0 | 90,791 | 5 | 181,582 |
No | output | 1 | 90,791 | 5 | 181,583 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961
Submitted Solution:
```
import math
X = int(input())
x = math.sqrt(X)
print(int(x) ** 2)
``` | instruction | 0 | 90,792 | 5 | 181,584 |
No | output | 1 | 90,792 | 5 | 181,585 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.
Constraints
* 1 ≤ X ≤ 1000
* X is an integer.
Input
Input is given from Standard Input in the following format:
X
Output
Print the largest perfect power that is at most X.
Examples
Input
10
Output
9
Input
1
Output
1
Input
999
Output
961
Submitted Solution:
```
X = int(input())
l = []
vall= []
for l1 in range(1,X+1):
for l2 in range(2,X+1):
l.append(l1 ** l2)
for val in l:
if(val<=X):
vall.append(val)
print(max(vall))
``` | instruction | 0 | 90,793 | 5 | 181,586 |
No | output | 1 | 90,793 | 5 | 181,587 |
Provide a correct Python 3 solution for this coding contest problem.
Consider an infinite sequence a_1, a_2, … Initially, the values of all the terms are 0, and from this state we will sequentially perform Q operations. The i-th operation (1 ≤ i ≤ Q) is as follows:
* For every positive integer j, add x_i to the value of a_{j × m_i}.
Find the value of the largest term after these Q operations.
Constraints
* 1 ≤ Q ≤ 299
* 2 ≤ m_i ≤ 300
* -10^6 ≤ x_i ≤ 10^6
* All m_i are distinct.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
Q
m_1 x_1
:
m_Q x_Q
Output
Print the value of the largest term after the Q operations.
Examples
Input
3
2 10
3 -20
6 15
Output
10
Input
3
10 -3
50 4
100 -5
Output
1
Input
5
56 114834
72 -149861
100 190757
192 -132693
240 133108
Output
438699 | instruction | 0 | 90,794 | 5 | 181,588 |
"Correct Solution:
```
from itertools import product
Q = int(input())
mxs = [tuple(map(int, input().split())) for _ in range(Q)]
p1s = [2,3,5,7,11,13,17]
nums = [9,6,4,3,3,3,3]
rangeNums = [range(num) for num in nums]
p2s = [19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293]
mx1s = []
mx2ss = [[] for _ in range(len(p2s))]
for m, x in mxs:
for i, p2 in enumerate(p2s):
if m % p2 == 0:
mx2ss[i].append((m, x))
break
else:
mx1s.append((m, x))
ans = 0
for es in product(*rangeNums):
f = 1
for p1, e in zip(p1s, es):
f *= p1**e
A = 0
for m1, x1 in mx1s:
if f % m1 == 0:
A += x1
for p2, mx2s in zip(p2s, mx2ss):
A2 = 0
for m2, x2 in mx2s:
if f*p2 % m2 == 0:
A2 += x2
if A2 > 0:
A += A2
ans = max(ans, A)
print(ans)
``` | output | 1 | 90,794 | 5 | 181,589 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider an infinite sequence a_1, a_2, … Initially, the values of all the terms are 0, and from this state we will sequentially perform Q operations. The i-th operation (1 ≤ i ≤ Q) is as follows:
* For every positive integer j, add x_i to the value of a_{j × m_i}.
Find the value of the largest term after these Q operations.
Constraints
* 1 ≤ Q ≤ 299
* 2 ≤ m_i ≤ 300
* -10^6 ≤ x_i ≤ 10^6
* All m_i are distinct.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
Q
m_1 x_1
:
m_Q x_Q
Output
Print the value of the largest term after the Q operations.
Examples
Input
3
2 10
3 -20
6 15
Output
10
Input
3
10 -3
50 4
100 -5
Output
1
Input
5
56 114834
72 -149861
100 190757
192 -132693
240 133108
Output
438699
Submitted Solution:
```
q = int(input())
mmm = dict(tuple(map(int, input().split())) for _ in range(q))
ans = 0
checked_m = set()
for m, x in sorted(mmm.items(), reverse=True):
if x >= 0:
checked_m.add(m)
continue
y = x
for cm in checked_m:
if cm % m == 0:
mmm[cm] += mmm[m]
del mmm[m]
print(sum(x for x in mmm.values() if x > 0))
``` | instruction | 0 | 90,795 | 5 | 181,590 |
No | output | 1 | 90,795 | 5 | 181,591 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Consider an infinite sequence a_1, a_2, … Initially, the values of all the terms are 0, and from this state we will sequentially perform Q operations. The i-th operation (1 ≤ i ≤ Q) is as follows:
* For every positive integer j, add x_i to the value of a_{j × m_i}.
Find the value of the largest term after these Q operations.
Constraints
* 1 ≤ Q ≤ 299
* 2 ≤ m_i ≤ 300
* -10^6 ≤ x_i ≤ 10^6
* All m_i are distinct.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
Q
m_1 x_1
:
m_Q x_Q
Output
Print the value of the largest term after the Q operations.
Examples
Input
3
2 10
3 -20
6 15
Output
10
Input
3
10 -3
50 4
100 -5
Output
1
Input
5
56 114834
72 -149861
100 190757
192 -132693
240 133108
Output
438699
Submitted Solution:
```
q = int(input())
mmm = dict(tuple(map(int, input().split())) for _ in range(q))
ans = 0
checked_m = set()
for m, x in sorted(mmm.items(), reverse=True):
if x >= 0:
checked_m.add(m)
continue
y = x
for cm in checked_m:
if cm % m == 0:
mmm[cm] += mmm[m]
print(sum(x for x in mmm.values() if x > 0))
``` | instruction | 0 | 90,796 | 5 | 181,592 |
No | output | 1 | 90,796 | 5 | 181,593 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1 | instruction | 0 | 90,797 | 5 | 181,594 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
n = int(input())
mod = pow(10, 9)+7
ct = [1]*(n+1)
for i in range(1, n+1):
ct[i] = ct[i-1]*i%mod
def comb(n, k):
res = ct[n]*pow(ct[n-k], mod-2, mod)%mod*pow(ct[k], mod-2, mod)%mod
return res
def main():
a = [int(x) for x in input().split()]
already = [-1]*n
for i in range(n+1):
if already[a[i]-1] != -1:
f, s = already[a[i]-1], n-i
break
already[a[i]-1] = i
ans = [0]*(n+1)
c = 1
for i in range(n+1):
c = c*(n+1-i)%mod*pow(i+1, mod-2, mod)%mod
ans[i] += c%mod
for i in range(n):
if s+f >= i:
ans[i] += mod-(comb(f+s, i))%mod
ans[i] %= mod
for a in ans:
print(a)
if __name__ == "__main__":
main()
``` | output | 1 | 90,797 | 5 | 181,595 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1 | instruction | 0 | 90,798 | 5 | 181,596 |
"Correct Solution:
```
N = int(input())
A = list(map(int,input().split()))
from collections import defaultdict
d = {}
for i,a in enumerate(A):
if a not in d:
d[a] = i
else:
l = d[a]
r = i
break
mod = 10**9+7
n = 100010
frac = [1]*(n+1)
finv = [1]*(n+1)
for i in range(n):
frac[i+1] = (i+1)*frac[i]%mod
finv[-1] = pow(frac[-1],mod-2,mod)
for i in range(1,n+1):
finv[n-i] = finv[n-i+1]*(n-i+1)%mod
def nCr(n,r):
if n<0 or r<0 or n<r: return 0
r = min(r,n-r)
return frac[n]*finv[n-r]*finv[r]%mod
ans = 0
for i in range(1,N+2):
ans = nCr(N+1,i)-nCr(N+l-r,i-1)
ans %= mod
print(ans)
``` | output | 1 | 90,798 | 5 | 181,597 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1 | instruction | 0 | 90,799 | 5 | 181,598 |
"Correct Solution:
```
MOD = 10 ** 9 + 7
MAXN = 100005
factorial = [1]
for i in range(1, MAXN + 1):
factorial.append(factorial[-1] * i % MOD)
inv_factorial = [-1] * (MAXN + 1)
inv_factorial[-1] = pow(factorial[-1], MOD-2, MOD)
for i in reversed(range(MAXN)):
inv_factorial[i] = inv_factorial[i + 1] * (i + 1) % MOD
def fact(n):
return factorial[n]
def nck(n, k):
if k > n or k < 0:
return 0
else:
return factorial[n]*inv_factorial[n - k]*inv_factorial[k]%MOD
def main():
n = int(input())
a = list(map(int,input().split()))
dic = {i:[] for i in range(1,n + 1)}
for i in range(n + 1):
dic[a[i]].append(i)
if len(dic[a[i]]) >= 2:
l,r = dic[a[i]][0],dic[a[i]][1]
break
r = n - r
print(n)
for i in range(2,n + 2):
print((nck(n + 1,i) - nck(l + r,i - 1) + MOD)%MOD)
if __name__ == '__main__':
main()
``` | output | 1 | 90,799 | 5 | 181,599 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1 | instruction | 0 | 90,800 | 5 | 181,600 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
dup = sum(a) - n * (n + 1) // 2
d1 = a.index(dup)
d2 = a.index(dup, d1 + 1)
N = n + 1
Ndup = d1 + n - d2
MOD = 10 ** 9 + 7
def power(x, n):
ans = 1
while n:
if n % 2 == 1:
ans = (ans * x) % MOD
x = (x * x) % MOD
n //= 2
return ans
# fack[k]: kの階乗
fact = [0 for i in range(N + 1)]
fact[0] = 1
for i in range(1, N + 1):
fact[i] = (fact[i - 1] * i) % MOD
# inv[k]: kの階乗の逆元
inv = [0 for i in range(N + 1)]
inv[N] = power(fact[N], MOD - 2) % MOD
for i in range(N - 1, -1, -1):
inv[i] = (inv[i + 1] * (i + 1)) % MOD
def comb(n, r):
if n < r:
return 0
else:
return (fact[n] * inv[n - r] * inv[r]) % MOD
for k in range(1, N + 1):
C = comb(N, k)
Cdup = comb(Ndup, k - 1)
print((C - Cdup) % MOD)
``` | output | 1 | 90,800 | 5 | 181,601 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1 | instruction | 0 | 90,801 | 5 | 181,602 |
"Correct Solution:
```
N, *X = map(int, open(0).read().split())
MAX = 10 ** 5 + 1
MOD = 10 ** 9 + 7
# Factorial
fac = [0] * (MAX + 1)
fac[0] = 1
fac[1] = 1
for i in range(2, MAX + 1):
fac[i] = fac[i - 1] * i % MOD
# Inverse factorial
finv = [0] * (MAX + 1)
finv[MAX] = pow(fac[MAX], MOD - 2, MOD)
for i in reversed(range(1, MAX + 1)):
finv[i - 1] = finv[i] * i % MOD
def comb(n, k):
if n < k:
return 0
return fac[n] * finv[n - k] * finv[k]
# Find indices of duplicated values
indices = [-1] * (N + 1)
for i in range(N + 1):
if indices[X[i]] < 0:
indices[X[i]] = i
else:
l = indices[X[i]]
r = i
break
for k in range(1, N + 2):
print((comb(N + 1, k) - comb(l + N - r, k - 1)) % MOD)
``` | output | 1 | 90,801 | 5 | 181,603 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1 | instruction | 0 | 90,802 | 5 | 181,604 |
"Correct Solution:
```
from collections import defaultdict
n = int(input()) + 1
a = list(map(int, input().split()))
mod = 10 ** 9 + 7
# 1を一つだけ選ぶやつは重複する可能性
d = defaultdict(int)
left = right = 0
for i in range(n):
if d[a[i]] > 0:
right = i
left = a.index(a[i])
break
d[a[i]] += 1
fac = [1] * (n + 1)
for i in range(1, n + 1):
fac[i] = fac[i - 1] * i % mod
def inv(x):
return pow(x, mod - 2, mod)
def c(n, k):
if n < 0 or k < 0 or n < k:
return 0
return fac[n] * inv(fac[n - k] * fac[k] % mod) % mod
left_len = left
right_len = n - right - 1
print(n - 1)
for i in range(2, n + 1):
ans = c(n, i) - (c(left_len + 1 + right_len, i) -
c(left_len + right_len, i))
print(ans % mod)
``` | output | 1 | 90,802 | 5 | 181,605 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1 | instruction | 0 | 90,803 | 5 | 181,606 |
"Correct Solution:
```
def mod_inv(n: int, mod: int)->int:
b, u, v = mod, 1, 0
while b > 0:
t = n // b
n -= t * b
u -= t * v
n, b = b, n
u, v = v, u
return (u+mod) % mod
def _11(N: int, A: list)->list:
MOD = 10**9 + 7
d = {}
l, r = 0, 0
for i, a in enumerate(A):
if a in d:
l, r = d[a], N-i
else:
d[a] = i
c1, c2 = [1]*(N+2), [1]*(N+2)
for i in range(N+1):
c1[i+1] = (c1[i] * (N+1-i) * mod_inv(i+1, MOD)) % MOD
c2[i+1] = (c2[i] * (l+r-i) * mod_inv(i+1, MOD)) % MOD
return [(c1[k+1]-c2[k]+MOD) % MOD for k in range(N+1)]
if __name__ == "__main__":
N = int(input())
A = [int(s) for s in input().split()]
ans = _11(N, A)
print('\n'.join(map(str, ans)))
``` | output | 1 | 90,803 | 5 | 181,607 |
Provide a correct Python 3 solution for this coding contest problem.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1 | instruction | 0 | 90,804 | 5 | 181,608 |
"Correct Solution:
```
import sys
input=sys.stdin.readline
def solve():
N = int(input())
d = {i:-1 for i in range(1, N+1)}
*l, = map(int, input().split())
MOD = 10**9+7
n = N+1
fac = [1]*(n+1)
rev = [1]*(n+1)
for i in range(1,n+1):
fac[i] = i*fac[i-1]%MOD
rev[i] = pow(fac[i], MOD-2, MOD)
comb = lambda a,b:(fac[a]*rev[a-b]*rev[b])%MOD if a>=b else 0
for i, j in enumerate(l):
if d[j] != -1:
break
d[j] = i
v = d[j]+N-i
for i in range(1, N+2):
print((comb(N+1, i)-comb(v, i-1))%MOD)
if __name__ == "__main__":
solve()
``` | output | 1 | 90,804 | 5 | 181,609 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
Submitted Solution:
```
MOD=10**9+7
from collections import Counter
def facinv(N):
fac,finv,inv=[0]*(N+1),[0]*(N+1),[0]*(N+1)
fac[0]=1;fac[1]=1;finv[0]=1;finv[1]=1;inv[1]=1
for i in range(2,N+1):
fac[i]=fac[i-1]*i%MOD
inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD
finv[i]=finv[i-1]*inv[i]%MOD
return fac,finv,inv
def COM(n,r):
if n<r or r<0:
return 0
else:
return ((fac[n]*finv[r])%MOD*finv[n-r])%MOD
N=int(input())
fac,finv,inv=facinv(N+1)
A=list(map(int,input().split()))
m=Counter(A).most_common()[0][0]
L,R=sorted([i for i in range(N+1) if A[i]==m])
R=N-R
for k in range(1,N+2):
print((COM(N+1,k)-COM(L+R,k-1)+MOD)%MOD)
``` | instruction | 0 | 90,805 | 5 | 181,610 |
Yes | output | 1 | 90,805 | 5 | 181,611 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
Submitted Solution:
```
from collections import Counter
n = int(input())
a = list(map(int, input().split()))
mod = 10 ** 9 + 7
MAX = 10 ** 5 + 10
fact = [1] * (MAX + 1)
for i in range(1, MAX + 1):
fact[i] = (fact[i-1] * i) % mod
inv = [1] * (MAX + 1)
for i in range(2, MAX + 1):
inv[i] = inv[mod % i] * (mod - mod // i) % mod
fact_inv = [1] * (MAX + 1)
for i in range(1, MAX + 1):
fact_inv[i] = fact_inv[i-1] * inv[i] % mod
def comb(n, r):
if n < r:
return 0
return fact[n] * fact_inv[n-r] * fact_inv[r] % mod
c = Counter(a)
for key, val in c.items():
if val == 2:
break
idx = []
for i, e in enumerate(a):
if e == key:
idx.append(i)
l = idx[0]
r = n - idx[1]
for k in range(1, n + 2):
ans = comb(n + 1, k) - comb(l + r, k - 1)
ans %= mod
print(ans)
``` | instruction | 0 | 90,806 | 5 | 181,612 |
Yes | output | 1 | 90,806 | 5 | 181,613 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
Submitted Solution:
```
from collections import Counter
N = int(input())
As = list(map(int, input().split()))
MOD = 10 ** 9 + 7
factorials = [1]
fact_invs = [1]
for i in range(1, N+2):
factorials.append((factorials[-1]*i) % MOD)
fact_invs.append(pow(factorials[-1], MOD-2, MOD))
fact_invs.append(1)
def combi(n, k):
if n < k:
return 0
ret = factorials[n]
ret *= fact_invs[k]
ret %= MOD
ret *= fact_invs[n-k]
return ret % MOD
ct = Counter(As)
mc = ct.most_common(1)[0][0]
L = R = None
for i, a in enumerate(As):
if a == mc:
if L is None:
L = i
else:
R = N - i
for k in range(1, N+2):
print((combi(N+1, k) - combi(L+R, k-1)) % MOD)
``` | instruction | 0 | 90,807 | 5 | 181,614 |
Yes | output | 1 | 90,807 | 5 | 181,615 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
Submitted Solution:
```
MOD = 10 ** 9 + 7
n = int(input())
a = list(map(int, input().split()))
lst = [-1] * n
# O(N)
for i in range(n + 1):
if lst[a[i] - 1] != -1:
first = lst[a[i] - 1]
second = i
break
lst[a[i] - 1] = i
# print (first, second)
left = first
right = n - second
U = 10 ** 5 + 1
def power_mod(a, n):
if n == 0:
return 1
x = power_mod(a//2)
def make_fact(fact, fact_inv):
for i in range(1, U + 1):
fact[i] = (fact[i - 1] * i) % MOD
fact_inv[U] = pow(fact[U], MOD - 2, MOD)
for i in range(U, 0, -1):
fact_inv[i - 1] = (fact_inv[i] * i) % MOD
def comb(n, k):
if k < 0 or n < k:
return 0
x = fact[n]
x *= fact_inv[k]
x %= MOD
x *= fact_inv[n - k]
x %= MOD
return x
fact = [1] * (U + 1)
fact_inv = [1] * (U + 1)
make_fact(fact, fact_inv)
for i in range(1, n + 2):
ans = comb(n + 1, i) - comb(left + right, i - 1)
print (ans % MOD)
``` | instruction | 0 | 90,808 | 5 | 181,616 |
Yes | output | 1 | 90,808 | 5 | 181,617 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
Submitted Solution:
```
from math import factorial
n = int(input())
a = [int(item) for item in input().split()]
def combination(n, r):
if n-r < 0:
return 0
return factorial(n) // (factorial(n-r) * factorial(r))
index = [-1] * (n+1)
l, r = 0, 0
for i, c in enumerate(a):
if index[c] == -1:
index[c] = i
else:
l = index[c]
r = i
for i in range(1, n+2):
print((combination(n+1, i) - combination(n+1 - (r-l) - 1, i-1))%(10**9 + 7))
``` | instruction | 0 | 90,809 | 5 | 181,618 |
No | output | 1 | 90,809 | 5 | 181,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
Submitted Solution:
```
MODULO = 10**9 + 7
def modulo(x):
return x % MODULO
n = int(input())
xs = list(map(int, input().split()))
def locate_dup(xs):
d = {}
for i,x in enumerate(xs):
if x in d:
return d[x], i
else:
d[x] = i
assert(False)
first, second = locate_dup(xs)
class X:
def __init__(self, first, second, length):
self.dup_first = first
self.dup_second = second
self.length = length
self.memo = {}
def C(self, k, pos):
v = self.memo.get((k, pos), None)
if v is None:
v = self.calcC(k, pos)
self.memo[(k, pos)] = v
return v
def calcC(self, k, pos):
if k <= 0 or pos >= self.length:
return 0
elif k == 1:
if pos <= self.dup_first:
return modulo(self.length - pos - 1)
else:
return modulo(self.length - pos)
else:
if pos == self.dup_first:
return modulo(self.C(k-1, pos+1) + self.C(k, pos+1) - self.C(k-1, self.dup_second + 1))
else:
return modulo(self.C(k-1, pos+1) + self.C(k, pos+1))
x = X(first, second, n+1)
for i in range(0, n+1):
for j in range(n+1, 1, -1):
x.C(i+1, j)
print(x.C(i+1, 0))
``` | instruction | 0 | 90,810 | 5 | 181,620 |
No | output | 1 | 90,810 | 5 | 181,621 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
Submitted Solution:
```
import sys
from collections import Counter
import numpy as np
sys.setrecursionlimit(2147483647)
INF = float('inf')
MOD = 10 ** 9 + 7
N = int(sys.stdin.readline())
A = list(map(int, sys.stdin.readline().split()))
def get_factorials(max, mod=None):
"""
階乗 0!, 1!, 2!, ..., max!
:param int max:
:param int mod:
:return:
"""
ret = [1]
n = 1
if mod:
for i in range(1, max + 1):
n *= i
n %= mod
ret.append(n)
else:
for i in range(1, max + 1):
n *= i
ret.append(n)
return ret
factorials = get_factorials(N + 1, MOD)
def ncr(n, r, mod=None):
"""
scipy.misc.comb または scipy.special.comb と同じ
組み合わせの数 nCr
:param int n:
:param int r:
:param int mod: 3 以上の素数であること
:rtype: int
"""
if n < r:
return 0
def inv(a):
"""
a の逆元
:param a:
:return:
"""
return pow(a, mod - 2, mod)
if mod:
return factorials[n] * inv(factorials[r]) * inv(factorials[n - r]) % mod
else:
return factorials[n] // factorials[r] // factorials[n - r]
# どことどこが一緒？
A = np.array(A)
dup, _ = Counter(A).most_common(1)[0]
L, r = np.where(A == dup)[0]
# dup より端から i 個選ぶ組み合わせ
sides = np.array([ncr(L + N - r, i, MOD) for i in range(N + 2)])
# 全部選んで選びすぎを引く
# dup を 1 つ選び、その他を dup より端から選ぶ組み合わせが重複する
ans = [ncr(N + 1, k, MOD) - sides[k - 1] for k in range(1, N + 2)]
print('\n'.join(map(str, ans)))
``` | instruction | 0 | 90,811 | 5 | 181,622 |
No | output | 1 | 90,811 | 5 | 181,623 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n. It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^5
* 1 \leq a_i \leq n
* Each of the integers 1,...,n appears in the sequence.
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}
Output
Print n+1 lines. The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.
Examples
Input
3
1 2 1 3
Output
3
5
4
1
Input
1
1 1
Output
1
1
Input
32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9
Output
32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1
Submitted Solution:
```
import sys
readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)
def main():
n = int(readline())
a = list(map(int, readline().split()))
dup = 0
for i in range(1, n + 2):
if a.count(i) == 2:
dup = i
first = a.index(dup)
second = a[first + 1:].index(dup) + first + 1
print(n)
p = first
q = (n + 1) - second - 1
c1 = n + 1
c2 = 1
for i in range(2, n + 2):
c1 *= (n + 1 - (i - 1))
c1 %= MOD
c1 *= pow(i, MOD - 2, MOD)
c1 %= MOD
c2 *= (p + q - (i - 2))
c2 %= MOD
c2 *= pow(i - 1, MOD - 2, MOD)
c2 %= MOD
print((c1 - c2) % MOD)
if __name__ == '__main__':
main()
``` | instruction | 0 | 90,812 | 5 | 181,624 |
No | output | 1 | 90,812 | 5 | 181,625 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid with R rows and C columns. We call the cell in the r-th row and c-th column (r，c).
Mr. Takahashi wrote non-negative integers into N of the cells, that is, he wrote a non-negative integer a_i into (r_i，c_i) for each i (1≤i≤N). After that he fell asleep.
Mr. Aoki found the grid and tries to surprise Mr. Takahashi by writing integers into all remaining cells. The grid must meet the following conditions to really surprise Mr. Takahashi.
* Condition 1: Each cell contains a non-negative integer.
* Condition 2: For any 2×2 square formed by cells on the grid, the sum of the top left and bottom right integers must always equal to the sum of the top right and bottom left integers.
Determine whether it is possible to meet those conditions by properly writing integers into all remaining cells.
Constraints
* 2≤R，C≤10^5
* 1≤N≤10^5
* 1≤r_i≤R
* 1≤c_i≤C
* (r_i，c_i) ≠ (r_j，c_j) (i≠j)
* a_i is an integer.
* 0≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
R C
N
r_1 c_1 a_1
r_2 c_2 a_2
:
r_N c_N a_N
Output
Print `Yes` if it is possible to meet the conditions by properly writing integers into all remaining cells. Otherwise, print `No`.
Examples
Input
2 2
3
1 1 0
1 2 10
2 1 20
Output
Yes
Input
2 3
5
1 1 0
1 2 10
1 3 20
2 1 30
2 3 40
Output
No
Input
2 2
3
1 1 20
1 2 10
2 1 0
Output
No
Input
3 3
4
1 1 0
1 3 10
3 1 10
3 3 20
Output
Yes
Input
2 2
4
1 1 0
1 2 10
2 1 30
2 2 20
Output
No
Submitted Solution:
```
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
from collections import defaultdict
import sys
sys.setrecursionlimit(10**6)
R, C = map(int, input().split())
N = int(input())
VectorSet = set()
Grid = defaultdict(list)
for i in range(N):
r, c, a = map(int, input().split())
Grid[("R", r)].append((("C", c), a))
Grid[("C", c)].append((("R", r), a))
VectorSet.add(("R", r))
VectorSet.add(("C", c))
def iteration(vector):
VectorSet.discard(vector)
for (v, a) in Grid[vector]:
temp = a - VectorCover[vector]
if (v in VectorCover):
if (temp != VectorCover[v]):
print("No")
exit()
else:
VectorCover[v] = temp
iteration(v)
while VectorSet:
vector = VectorSet.pop()
VectorCover = dict()
VectorCover[vector] = 0
iteration(vector)
minR = min(a for (p, a) in VectorCover.items() if (p[0] == "R"))
minC = min(a for (p, a) in VectorCover.items() if (p[0] == "C"))
if minR + minC < 0:
print("No")
exit()
print("Yes")
``` | instruction | 0 | 90,837 | 5 | 181,674 |
Yes | output | 1 | 90,837 | 5 | 181,675 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid with R rows and C columns. We call the cell in the r-th row and c-th column (r，c).
Mr. Takahashi wrote non-negative integers into N of the cells, that is, he wrote a non-negative integer a_i into (r_i，c_i) for each i (1≤i≤N). After that he fell asleep.
Mr. Aoki found the grid and tries to surprise Mr. Takahashi by writing integers into all remaining cells. The grid must meet the following conditions to really surprise Mr. Takahashi.
* Condition 1: Each cell contains a non-negative integer.
* Condition 2: For any 2×2 square formed by cells on the grid, the sum of the top left and bottom right integers must always equal to the sum of the top right and bottom left integers.
Determine whether it is possible to meet those conditions by properly writing integers into all remaining cells.
Constraints
* 2≤R，C≤10^5
* 1≤N≤10^5
* 1≤r_i≤R
* 1≤c_i≤C
* (r_i，c_i) ≠ (r_j，c_j) (i≠j)
* a_i is an integer.
* 0≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
R C
N
r_1 c_1 a_1
r_2 c_2 a_2
:
r_N c_N a_N
Output
Print `Yes` if it is possible to meet the conditions by properly writing integers into all remaining cells. Otherwise, print `No`.
Examples
Input
2 2
3
1 1 0
1 2 10
2 1 20
Output
Yes
Input
2 3
5
1 1 0
1 2 10
1 3 20
2 1 30
2 3 40
Output
No
Input
2 2
3
1 1 20
1 2 10
2 1 0
Output
No
Input
3 3
4
1 1 0
1 3 10
3 1 10
3 3 20
Output
Yes
Input
2 2
4
1 1 0
1 2 10
2 1 30
2 2 20
Output
No
Submitted Solution:
```
from collections import defaultdict
import sys
sys.setrecursionlimit(10**6)
def ReadInput():
return [int(i) for i in input().split(" ")]
(R, C) = ReadInput()
N = int(input())
VectorSet = set()
Grid = defaultdict(list)
for i in range(N):
(r, c, a) = ReadInput()
Grid[("R", r)].append((("C", c), a))
Grid[("C", c)].append((("R", r), a))
VectorSet.add(("R", r))
VectorSet.add(("C", c))
def iteration(vector):
VectorSet.discard(vector)
for (v, a) in Grid[vector]:
temp = a - VectorCover[vector]
if (v in VectorCover):
if(temp is not VectorCover[v]):
print("No")
exit()
else:
VectorCover[v] = temp
iteration(v)
while(len(VectorSet) is not 0):
vector = VectorSet.pop()
VectorCover = dict()
VectorCover[vector] = 0
iteration(vector)
minR = min(a for (p, a) in VectorCover.items() if (p[0] is "R"))
minC = min(a for (p, a) in VectorCover.items() if (p[0] is "C"))
if (minR + minC < 0):
print("No")
exit()
print("Yes")
``` | instruction | 0 | 90,839 | 5 | 181,678 |
No | output | 1 | 90,839 | 5 | 181,679 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid with R rows and C columns. We call the cell in the r-th row and c-th column (r，c).
Mr. Takahashi wrote non-negative integers into N of the cells, that is, he wrote a non-negative integer a_i into (r_i，c_i) for each i (1≤i≤N). After that he fell asleep.
Mr. Aoki found the grid and tries to surprise Mr. Takahashi by writing integers into all remaining cells. The grid must meet the following conditions to really surprise Mr. Takahashi.
* Condition 1: Each cell contains a non-negative integer.
* Condition 2: For any 2×2 square formed by cells on the grid, the sum of the top left and bottom right integers must always equal to the sum of the top right and bottom left integers.
Determine whether it is possible to meet those conditions by properly writing integers into all remaining cells.
Constraints
* 2≤R，C≤10^5
* 1≤N≤10^5
* 1≤r_i≤R
* 1≤c_i≤C
* (r_i，c_i) ≠ (r_j，c_j) (i≠j)
* a_i is an integer.
* 0≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
R C
N
r_1 c_1 a_1
r_2 c_2 a_2
:
r_N c_N a_N
Output
Print `Yes` if it is possible to meet the conditions by properly writing integers into all remaining cells. Otherwise, print `No`.
Examples
Input
2 2
3
1 1 0
1 2 10
2 1 20
Output
Yes
Input
2 3
5
1 1 0
1 2 10
1 3 20
2 1 30
2 3 40
Output
No
Input
2 2
3
1 1 20
1 2 10
2 1 0
Output
No
Input
3 3
4
1 1 0
1 3 10
3 1 10
3 3 20
Output
Yes
Input
2 2
4
1 1 0
1 2 10
2 1 30
2 2 20
Output
No
Submitted Solution:
```
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# D-Grid and Integers
from collections import defaultdict
def ReadInput():
return [int(i) for i in input().split(" ")]
(R, C) = ReadInput()
N = int(input())
RowIdx = set()
ColIdx = set()
Grid = defaultdict(list)
RowGrid = defaultdict(list)
ColGrid = defaultdict(list)
for i in range(N):
(r, c, a) = ReadInput()
RowGrid[r].append(c)
ColGrid[c].append(r)
Grid[(r, c)] = a
RowIdx.add(r)
ColIdx.add(c)
print(RowIdx)
print(RowGrid)
print(ColGrid)
print(Grid)
fresh = 1
while(fresh == 1):
fresh = 0
for row in RowIdx:
if (len(RowGrid[row]) == 1):
continue
TempRow = RowGrid[row]
TempColGrid = ColGrid
for pointer in TempRow:
TempCol = TempRow
TempCol.remove(pointer)
for pair in TempCol:
dif = Grid[(row, pointer)] - Grid[(row, pair)]
ObjCol = TempColGrid[pointer]
print('pair is', pair)
print('row equal', row)
print('ObjCol equal', ObjCol)
print('TempColGrid[pointer] is', TempColGrid[pointer])
if row in ObjCol:
ObjCol.remove(row)
for obj in ObjCol:
val = Grid[(obj, pointer)]- dif
if (val < 0):
print("No")
exit()
if ((obj, pair) in Grid):
if (val != Grid[(obj, pair)]):
print("No");
exit()
else:
Grid[(obj, pair)] = val
RowGrid[obj].append(pair)
ColGrid[pair].append(obj)
fresh = 1
print("Yes")
``` | instruction | 0 | 90,840 | 5 | 181,680 |
No | output | 1 | 90,840 | 5 | 181,681 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid with R rows and C columns. We call the cell in the r-th row and c-th column (r，c).
Mr. Takahashi wrote non-negative integers into N of the cells, that is, he wrote a non-negative integer a_i into (r_i，c_i) for each i (1≤i≤N). After that he fell asleep.
Mr. Aoki found the grid and tries to surprise Mr. Takahashi by writing integers into all remaining cells. The grid must meet the following conditions to really surprise Mr. Takahashi.
* Condition 1: Each cell contains a non-negative integer.
* Condition 2: For any 2×2 square formed by cells on the grid, the sum of the top left and bottom right integers must always equal to the sum of the top right and bottom left integers.
Determine whether it is possible to meet those conditions by properly writing integers into all remaining cells.
Constraints
* 2≤R，C≤10^5
* 1≤N≤10^5
* 1≤r_i≤R
* 1≤c_i≤C
* (r_i，c_i) ≠ (r_j，c_j) (i≠j)
* a_i is an integer.
* 0≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
R C
N
r_1 c_1 a_1
r_2 c_2 a_2
:
r_N c_N a_N
Output
Print `Yes` if it is possible to meet the conditions by properly writing integers into all remaining cells. Otherwise, print `No`.
Examples
Input
2 2
3
1 1 0
1 2 10
2 1 20
Output
Yes
Input
2 3
5
1 1 0
1 2 10
1 3 20
2 1 30
2 3 40
Output
No
Input
2 2
3
1 1 20
1 2 10
2 1 0
Output
No
Input
3 3
4
1 1 0
1 3 10
3 1 10
3 3 20
Output
Yes
Input
2 2
4
1 1 0
1 2 10
2 1 30
2 2 20
Output
No
Submitted Solution:
```
from collections import defaultdict
def readInput():
return [int(i) for i in input().split(" ")]
(R, C) = readInput()
N = int(input())
rowIdx = set()
grid = defaultdict(lambda:None)
rowGrid = defaultdict(set)
for i in range(N):
(r, c, a) = readInput()
r -= 1
c -= 1
rowGrid[r].add(c)
grid[(r, c)] = a
rowIdx.add(r)
pairIdx = rowIdx.copy()
for i in rowIdx:
pairIdx.remove(i)
for j in pairIdx:
tempRow = rowGrid[i]
tempPair = rowGrid[j]
mark = 1
for k in tempRow:
if (grid[(j, k)] != None):
diff = grid[(i, k)] - grid[(j, k)]
mark = 0
if (mark is 1):
continue
for m in tempRow:
anchor = grid[(i, m)]
anchorP = grid[(j, m)]
if (anchorP is None and anchor < diff):
print('No')
exit()
elif (anchorP is not None and anchor - anchorP != diff):
print('No')
exit()
for n in tempPair:
anchor = grid[(j, n)]
anchorP = grid[(i, n)]
if (anchorP is None and anchor < -diff):
print('No')
exit()
print('Yes')
``` | instruction | 0 | 90,841 | 5 | 181,682 |
No | output | 1 | 90,841 | 5 | 181,683 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a grid with R rows and C columns. We call the cell in the r-th row and c-th column (r，c).
Mr. Takahashi wrote non-negative integers into N of the cells, that is, he wrote a non-negative integer a_i into (r_i，c_i) for each i (1≤i≤N). After that he fell asleep.
Mr. Aoki found the grid and tries to surprise Mr. Takahashi by writing integers into all remaining cells. The grid must meet the following conditions to really surprise Mr. Takahashi.
* Condition 1: Each cell contains a non-negative integer.
* Condition 2: For any 2×2 square formed by cells on the grid, the sum of the top left and bottom right integers must always equal to the sum of the top right and bottom left integers.
Determine whether it is possible to meet those conditions by properly writing integers into all remaining cells.
Constraints
* 2≤R，C≤10^5
* 1≤N≤10^5
* 1≤r_i≤R
* 1≤c_i≤C
* (r_i，c_i) ≠ (r_j，c_j) (i≠j)
* a_i is an integer.
* 0≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
R C
N
r_1 c_1 a_1
r_2 c_2 a_2
:
r_N c_N a_N
Output
Print `Yes` if it is possible to meet the conditions by properly writing integers into all remaining cells. Otherwise, print `No`.
Examples
Input
2 2
3
1 1 0
1 2 10
2 1 20
Output
Yes
Input
2 3
5
1 1 0
1 2 10
1 3 20
2 1 30
2 3 40
Output
No
Input
2 2
3
1 1 20
1 2 10
2 1 0
Output
No
Input
3 3
4
1 1 0
1 3 10
3 1 10
3 3 20
Output
Yes
Input
2 2
4
1 1 0
1 2 10
2 1 30
2 2 20
Output
No
Submitted Solution:
```
from collections import defaultdict
R, C = map(int, input().split())
G = defaultdict(lambda:-1)
n = int(input())
RCA = [list(map(int, input().split())) for _ in range(n)]
for r, c, a in RCA:
G[(r, c)] = a
D = [(-1, -1, -1, 0), (-1, -1, 0, -1), (-1, 1, -1, 0), (-1, 1, 0, 1), (1, -1, 1, 0), (1, -1, 0, -1), (1, 1, 1, 0), (1, 1, 0, 1)]
for r, c, a in RCA:
for w, x, y, z in D:
if G[(r+w, c+x)]!=-1 and G[(r+y, c+z)]!=-1:
if G[(r+(w^y), c+(x^z))]==-1:
G[(r+(w^y), c+(x^z))] = G[(r, c)]+G[(r+w, c+x)]-G[(r+y, c+z)]
if G[(r+(w^y), c+(x^z))] < 0:
print("No")
exit()
else:
if G[(r+(w^y), c+(x^z))] != G[(r, c)]+G[(r+w, c+x)]-G[(r+y, c+z)]:
print("No")
exit()
print("Yes")
``` | instruction | 0 | 90,842 | 5 | 181,684 |
No | output | 1 | 90,842 | 5 | 181,685 |
Provide a correct Python 3 solution for this coding contest problem.
Example
Input
5 5 4
6
3 2
4 2
5 2
1 4
3 4
5 4
Output
6 | instruction | 0 | 90,931 | 5 | 181,862 |
"Correct Solution:
```
from collections import defaultdict
import sys
readline = sys.stdin.readline
write = sys.stdout.write
def solve():
W, H, K = map(int, readline().split())
N = int(readline())
mp = defaultdict(lambda:defaultdict(int))
for i in range(N):
x, y = map(int, readline().split())
if y % 2 == 1:
continue
if x % 2 == 1:
mp[y][x//2] |= 1
if x < W:
mp[y][x//2+1] |= 4
else:
mp[y][x//2] |= 2
if K < W//2:
write("-1\n")
return
K -= W//2+1
r = 0
for y, mp_xs in mp.items():
*S, = mp_xs.items()
S.sort()
a = 0; b = 10**9
prv = -1
for x, bs in S:
if x - prv > 1:
a = b = min(a, b)
v0 = ((bs & 1) > 0); v1 = ((bs & 2) > 0); v2 = ((bs & 4) > 0)
a, b = min(a + v0, b + min(v0+v2, 2*v1)), min(a, b + v2)
prv = x
if prv < W // 2:
c = min(a, b)
else:
c = a
r += c
ans = max((W//2+1)*(H//2) + max(r - K, 0) - K, 0)
write("%d\n" % ans)
solve()
``` | output | 1 | 90,931 | 5 | 181,863 |
Provide a correct Python 3 solution for this coding contest problem.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0 | instruction | 0 | 90,937 | 5 | 181,874 |
"Correct Solution:
```
q = int(input())
s = set()
for i in range(q):
x, y = map(int, input().split())
if x == 0:
s.add(y)
print(len(s))
else:
if y in s:
print(1)
else:
print(0)
``` | output | 1 | 90,937 | 5 | 181,875 |
Provide a correct Python 3 solution for this coding contest problem.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0 | instruction | 0 | 90,938 | 5 | 181,876 |
"Correct Solution:
```
numset = set([])
q = int(input())
for i in range(q):
query, x = list(map(int, input().split(' ')))
if query == 0:
numset.add(x)
print(len(numset))
else:
if set([x]).issubset(numset):
print(1)
else:
print(0)
``` | output | 1 | 90,938 | 5 | 181,877 |
Provide a correct Python 3 solution for this coding contest problem.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0 | instruction | 0 | 90,939 | 5 | 181,878 |
"Correct Solution:
```
#空セットを作り標準入力をする
num_list = set()
for _ in range(int(input())):
a,b = map(int,input().split())
#aが0のときはセットにbを加え要素数を出力する
if a == 0:
num_list.add(b)
print(len(num_list))
#aが1のときbがセットの中にあるなら1ないなら0を出力する
elif a == 1:print(1 if b in num_list else 0)
``` | output | 1 | 90,939 | 5 | 181,879 |
Provide a correct Python 3 solution for this coding contest problem.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0 | instruction | 0 | 90,940 | 5 | 181,880 |
"Correct Solution:
```
S = set()
q = int(input())
for _ in range(q):
command, *list_num = input().split()
x = int(list_num[0])
if command == "0":
# insert(x)
S.add(x)
print(len(S))
elif command == "1":
# find(x)
if x in S:
print(1)
else:
print(0)
else:
raise
``` | output | 1 | 90,940 | 5 | 181,881 |
Provide a correct Python 3 solution for this coding contest problem.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0 | instruction | 0 | 90,941 | 5 | 181,882 |
"Correct Solution:
```
if __name__ == '__main__':
n = int(input())
S = set()
for _ in range(n):
x,y = map(int,input().split())
if x == 0:
S.add(y)
print(len(S))
else:
if y in S:
print("1")
else:
print("0")
``` | output | 1 | 90,941 | 5 | 181,883 |
Provide a correct Python 3 solution for this coding contest problem.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0 | instruction | 0 | 90,942 | 5 | 181,884 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
"""
Set - Set: Search
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP2_7_A&lang=jp
"""
s = set()
for _ in range(int(input())):
q, x = input().split()
if q == '0':
s.add(x)
print(len(s))
else:
print(int(x in s))
``` | output | 1 | 90,942 | 5 | 181,885 |
Provide a correct Python 3 solution for this coding contest problem.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0 | instruction | 0 | 90,943 | 5 | 181,886 |
"Correct Solution:
```
import math
class LinearProbingIntSet:
def __init__(self):
self.count = 0
self.size = 3
self.keys = [None] * self.size
def add(self, key):
i = self._hash(key)
for j in range(self.size):
k = (i + j) % self.size
if self.keys[k] is None:
self.keys[k] = key
self.count += 1
break
elif self.keys[k] == key:
break
else:
raise RuntimeError('set is full')
if self.count > self.size // 2:
self._resize(int(2 ** (math.log2(self.size+1)+1)) - 1)
def __contains__(self, key):
i = self._hash(key)
for j in range(self.size):
k = (i + j) % self.size
if self.keys[k] is None:
return False
elif self.keys[k] == key:
return True
raise RuntimeError('set is full')
def _hash(self, key):
return key % self.size
def _resize(self, size):
old_keys = self.keys
self.count = 0
self.size = size
self.keys = [None] * self.size
for key in old_keys:
if key is None:
continue
self.add(key)
def run():
q = int(input())
s = LinearProbingIntSet()
for _ in range(q):
command, value = [int(x) for x in input().split()]
if command == 0:
s.add(value)
print(s.count)
elif command == 1:
if value in s:
print(1)
else:
print(0)
else:
raise ValueError('invalid command')
if __name__ == '__main__':
run()
``` | output | 1 | 90,943 | 5 | 181,887 |
Provide a correct Python 3 solution for this coding contest problem.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0 | instruction | 0 | 90,944 | 5 | 181,888 |
"Correct Solution:
```
def resolve():
import sys
input = sys.stdin.readline
q = int(input())
ans = set()
for _ in range(q):
q = [int(i) for i in input().split()]
x = q[1]
if q[0] == 0:
ans.add(x)
print(len(ans))
else:
if x in ans:
print(1)
else:
print(0)
resolve()
``` | output | 1 | 90,944 | 5 | 181,889 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0
Submitted Solution:
```
#!/usr/bin/env python
# -*- coding: utf-8 -*-
#
# FileName: set:search
# CreatedDate: 2020-06-10 21:03:41 +0900
# LastModified: 2020-06-10 21:13:52 +0900
#
import os
import sys
#import numpy as np
#import pandas as pd
def main():
q=int(input())
a=set()
for _ in range(q):
command,x=map(int,input().split())
# print(command,x)
if command==0:
a.add(int(x))
print(len(a))
else:
if int(x) in a:
print(1)
else:
print(0)
if __name__ == "__main__":
main()
``` | instruction | 0 | 90,945 | 5 | 181,890 |
Yes | output | 1 | 90,945 | 5 | 181,891 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0
Submitted Solution:
```
import bisect
S=[]
def insert(S,count,x):
y=bisect.bisect(S,x)
if y-1<0 or S[y-1]!=x:
S.insert(y,x)
count+=1
print(count)
return S,count
def find(S,x):
y=bisect.bisect(S,x)
if y-1>=0 and S[y-1]==x:
print(1)
else:
print(0)
q=int(input())
count=0
for i in range(q):
query=list(map(int,input().split()))
if query[0]==0:
S,count=insert(S,count,query[1])
else:
find(S,query[1])
``` | instruction | 0 | 90,946 | 5 | 181,892 |
Yes | output | 1 | 90,946 | 5 | 181,893 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0
Submitted Solution:
```
# coding=utf-8
Q = int(input())
S = set()
for i in range(Q):
qtype, number = map(int, input().split())
if qtype == 0:
S.add(number)
print(len(S))
if qtype == 1:
if number in S:
print(1)
else:
print(0)
``` | instruction | 0 | 90,947 | 5 | 181,894 |
Yes | output | 1 | 90,947 | 5 | 181,895 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a set $S$ of integers, perform a sequence of the following operations. Note that each value in $S$ must be unique.
* insert($x$): Insert $x$ to $S$ and report the number of elements in $S$ after the operation.
* find($x$): Report the number of $x$ in $S$ (0 or 1).
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq x \leq 1,000,000,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $x$
or
1 $x$
where the first digits 0 and 1 represent insert and find operations respectively.
Output
For each insert operation, print the number of elements in $S$.
For each find operation, print the number of specified elements in $S$.
Example
Input
7
0 1
0 2
0 3
0 2
0 4
1 3
1 10
Output
1
2
3
3
4
1
0
Submitted Solution:
```
q = int(input())
num = set()
for _ in range(q):
query, x = map(int, input().split())
if query == 0:
num.add(x)
print(len(num))
elif query == 1:
if x in num:
print(1)
else:
print(0)
``` | instruction | 0 | 90,948 | 5 | 181,896 |
Yes | output | 1 | 90,948 | 5 | 181,897 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ivan has number b. He is sorting through the numbers a from 1 to 10^{18}, and for every a writes ([a, b])/(a) on blackboard. Here [a, b] stands for least common multiple of a and b. Ivan is very lazy, that's why this task bored him soon. But he is interested in how many different numbers he would write on the board if he would finish the task. Help him to find the quantity of different numbers he would write on the board.
Input
The only line contains one integer — b (1 ≤ b ≤ 10^{10}).
Output
Print one number — answer for the problem.
Examples
Input
1
Output
1
Input
2
Output
2
Note
In the first example [a, 1] = a, therefore ([a, b])/(a) is always equal to 1.
In the second example [a, 2] can be equal to a or 2 ⋅ a depending on parity of a. ([a, b])/(a) can be equal to 1 and 2.
Submitted Solution:
```
from math import*
n=int(input())
summ=0
for i in range(1, int(sqrt(n))+1):
if n%i==0 and i!= sqrt(n):
summ+=2
if i==sqrt(n):
summ+=1
print(summ)
``` | instruction | 0 | 90,959 | 5 | 181,918 |
Yes | output | 1 | 90,959 | 5 | 181,919 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ivan has number b. He is sorting through the numbers a from 1 to 10^{18}, and for every a writes ([a, b])/(a) on blackboard. Here [a, b] stands for least common multiple of a and b. Ivan is very lazy, that's why this task bored him soon. But he is interested in how many different numbers he would write on the board if he would finish the task. Help him to find the quantity of different numbers he would write on the board.
Input
The only line contains one integer — b (1 ≤ b ≤ 10^{10}).
Output
Print one number — answer for the problem.
Examples
Input
1
Output
1
Input
2
Output
2
Note
In the first example [a, 1] = a, therefore ([a, b])/(a) is always equal to 1.
In the second example [a, 2] can be equal to a or 2 ⋅ a depending on parity of a. ([a, b])/(a) can be equal to 1 and 2.
Submitted Solution:
```
import math
n = int(input())
ans = 0
for i in range(1, int(math.sqrt(n)) + 1):
if n % i == 0:
if n // i == i:
ans += 1
else:
ans += 2
print(ans)
``` | instruction | 0 | 90,960 | 5 | 181,920 |
Yes | output | 1 | 90,960 | 5 | 181,921 |
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