text stringlengths 198 433k | conversation_id int64 0 109k |
|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are quite a lot of ways to have fun with inflatable balloons. For example, you can fill them with water and see what happens.
Grigory and Andrew have the same opinion. So, once upon a time, they went to the shop and bought n packets with inflatable balloons, where i-th of them has exactly a_i balloons inside.
They want to divide the balloons among themselves. In addition, there are several conditions to hold:
* Do not rip the packets (both Grigory and Andrew should get unbroken packets);
* Distribute all packets (every packet should be given to someone);
* Give both Grigory and Andrew at least one packet;
* To provide more fun, the total number of balloons in Grigory's packets should not be equal to the total number of balloons in Andrew's packets.
Help them to divide the balloons or determine that it's impossible under these conditions.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 10) — the number of packets with balloons.
The second line contains n integers: a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000) — the number of balloons inside the corresponding packet.
Output
If it's impossible to divide the balloons satisfying the conditions above, print -1.
Otherwise, print an integer k — the number of packets to give to Grigory followed by k distinct integers from 1 to n — the indices of those. The order of packets doesn't matter.
If there are multiple ways to divide balloons, output any of them.
Examples
Input
3
1 2 1
Output
2
1 2
Input
2
5 5
Output
-1
Input
1
10
Output
-1
Note
In the first test Grigory gets 3 balloons in total while Andrey gets 1.
In the second test there's only one way to divide the packets which leads to equal numbers of balloons.
In the third test one of the boys won't get a packet at all.
Submitted Solution:
```
n=int(input())
x = list(map(int, input().split(" ")))
if n==1 or x.count(min(x))==2==len(x):
print(-1)
else:
print(1,x.index(min(x))+1,sep="\n")
```
Yes
| 13,100 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are quite a lot of ways to have fun with inflatable balloons. For example, you can fill them with water and see what happens.
Grigory and Andrew have the same opinion. So, once upon a time, they went to the shop and bought n packets with inflatable balloons, where i-th of them has exactly a_i balloons inside.
They want to divide the balloons among themselves. In addition, there are several conditions to hold:
* Do not rip the packets (both Grigory and Andrew should get unbroken packets);
* Distribute all packets (every packet should be given to someone);
* Give both Grigory and Andrew at least one packet;
* To provide more fun, the total number of balloons in Grigory's packets should not be equal to the total number of balloons in Andrew's packets.
Help them to divide the balloons or determine that it's impossible under these conditions.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 10) — the number of packets with balloons.
The second line contains n integers: a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000) — the number of balloons inside the corresponding packet.
Output
If it's impossible to divide the balloons satisfying the conditions above, print -1.
Otherwise, print an integer k — the number of packets to give to Grigory followed by k distinct integers from 1 to n — the indices of those. The order of packets doesn't matter.
If there are multiple ways to divide balloons, output any of them.
Examples
Input
3
1 2 1
Output
2
1 2
Input
2
5 5
Output
-1
Input
1
10
Output
-1
Note
In the first test Grigory gets 3 balloons in total while Andrey gets 1.
In the second test there's only one way to divide the packets which leads to equal numbers of balloons.
In the third test one of the boys won't get a packet at all.
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
if n == 1:
print (-1)
elif n == 2 and a[0] == a[1]:
print (-1)
else:
m = min(a)
id = a.index(m) + 1
print (1)
print (id)
```
Yes
| 13,101 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are quite a lot of ways to have fun with inflatable balloons. For example, you can fill them with water and see what happens.
Grigory and Andrew have the same opinion. So, once upon a time, they went to the shop and bought n packets with inflatable balloons, where i-th of them has exactly a_i balloons inside.
They want to divide the balloons among themselves. In addition, there are several conditions to hold:
* Do not rip the packets (both Grigory and Andrew should get unbroken packets);
* Distribute all packets (every packet should be given to someone);
* Give both Grigory and Andrew at least one packet;
* To provide more fun, the total number of balloons in Grigory's packets should not be equal to the total number of balloons in Andrew's packets.
Help them to divide the balloons or determine that it's impossible under these conditions.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 10) — the number of packets with balloons.
The second line contains n integers: a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000) — the number of balloons inside the corresponding packet.
Output
If it's impossible to divide the balloons satisfying the conditions above, print -1.
Otherwise, print an integer k — the number of packets to give to Grigory followed by k distinct integers from 1 to n — the indices of those. The order of packets doesn't matter.
If there are multiple ways to divide balloons, output any of them.
Examples
Input
3
1 2 1
Output
2
1 2
Input
2
5 5
Output
-1
Input
1
10
Output
-1
Note
In the first test Grigory gets 3 balloons in total while Andrey gets 1.
In the second test there's only one way to divide the packets which leads to equal numbers of balloons.
In the third test one of the boys won't get a packet at all.
Submitted Solution:
```
n=int(input())
arr=list(map(int,input().strip().split(' ')))
m=min(arr)
ind=arr.index(m)
if(n==1):
print(-1)
elif(n==2 and arr[0]==arr[1]):
print(-1)
else:
print(1)
print(ind+1)
```
Yes
| 13,102 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are quite a lot of ways to have fun with inflatable balloons. For example, you can fill them with water and see what happens.
Grigory and Andrew have the same opinion. So, once upon a time, they went to the shop and bought n packets with inflatable balloons, where i-th of them has exactly a_i balloons inside.
They want to divide the balloons among themselves. In addition, there are several conditions to hold:
* Do not rip the packets (both Grigory and Andrew should get unbroken packets);
* Distribute all packets (every packet should be given to someone);
* Give both Grigory and Andrew at least one packet;
* To provide more fun, the total number of balloons in Grigory's packets should not be equal to the total number of balloons in Andrew's packets.
Help them to divide the balloons or determine that it's impossible under these conditions.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 10) — the number of packets with balloons.
The second line contains n integers: a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000) — the number of balloons inside the corresponding packet.
Output
If it's impossible to divide the balloons satisfying the conditions above, print -1.
Otherwise, print an integer k — the number of packets to give to Grigory followed by k distinct integers from 1 to n — the indices of those. The order of packets doesn't matter.
If there are multiple ways to divide balloons, output any of them.
Examples
Input
3
1 2 1
Output
2
1 2
Input
2
5 5
Output
-1
Input
1
10
Output
-1
Note
In the first test Grigory gets 3 balloons in total while Andrey gets 1.
In the second test there's only one way to divide the packets which leads to equal numbers of balloons.
In the third test one of the boys won't get a packet at all.
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
if n==1 or n==2 and a[0]==a[1]:
print(-1)
else:
print(1)
print(a.index(min(a))+1)
```
Yes
| 13,103 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are quite a lot of ways to have fun with inflatable balloons. For example, you can fill them with water and see what happens.
Grigory and Andrew have the same opinion. So, once upon a time, they went to the shop and bought n packets with inflatable balloons, where i-th of them has exactly a_i balloons inside.
They want to divide the balloons among themselves. In addition, there are several conditions to hold:
* Do not rip the packets (both Grigory and Andrew should get unbroken packets);
* Distribute all packets (every packet should be given to someone);
* Give both Grigory and Andrew at least one packet;
* To provide more fun, the total number of balloons in Grigory's packets should not be equal to the total number of balloons in Andrew's packets.
Help them to divide the balloons or determine that it's impossible under these conditions.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 10) — the number of packets with balloons.
The second line contains n integers: a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000) — the number of balloons inside the corresponding packet.
Output
If it's impossible to divide the balloons satisfying the conditions above, print -1.
Otherwise, print an integer k — the number of packets to give to Grigory followed by k distinct integers from 1 to n — the indices of those. The order of packets doesn't matter.
If there are multiple ways to divide balloons, output any of them.
Examples
Input
3
1 2 1
Output
2
1 2
Input
2
5 5
Output
-1
Input
1
10
Output
-1
Note
In the first test Grigory gets 3 balloons in total while Andrey gets 1.
In the second test there's only one way to divide the packets which leads to equal numbers of balloons.
In the third test one of the boys won't get a packet at all.
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
a.sort()
if (a[0] == sum(a[:1]) or len(a) <= 1):
print(-1)
else:
print(a[0])
print(*a[1:])
```
No
| 13,104 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are quite a lot of ways to have fun with inflatable balloons. For example, you can fill them with water and see what happens.
Grigory and Andrew have the same opinion. So, once upon a time, they went to the shop and bought n packets with inflatable balloons, where i-th of them has exactly a_i balloons inside.
They want to divide the balloons among themselves. In addition, there are several conditions to hold:
* Do not rip the packets (both Grigory and Andrew should get unbroken packets);
* Distribute all packets (every packet should be given to someone);
* Give both Grigory and Andrew at least one packet;
* To provide more fun, the total number of balloons in Grigory's packets should not be equal to the total number of balloons in Andrew's packets.
Help them to divide the balloons or determine that it's impossible under these conditions.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 10) — the number of packets with balloons.
The second line contains n integers: a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000) — the number of balloons inside the corresponding packet.
Output
If it's impossible to divide the balloons satisfying the conditions above, print -1.
Otherwise, print an integer k — the number of packets to give to Grigory followed by k distinct integers from 1 to n — the indices of those. The order of packets doesn't matter.
If there are multiple ways to divide balloons, output any of them.
Examples
Input
3
1 2 1
Output
2
1 2
Input
2
5 5
Output
-1
Input
1
10
Output
-1
Note
In the first test Grigory gets 3 balloons in total while Andrey gets 1.
In the second test there's only one way to divide the packets which leads to equal numbers of balloons.
In the third test one of the boys won't get a packet at all.
Submitted Solution:
```
a=int(input());b=sorted(map(int,input().split()));print(*[[-1],["1\n1"]][a>1 and b[0]!=sum(b)-b[0]])
```
No
| 13,105 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are quite a lot of ways to have fun with inflatable balloons. For example, you can fill them with water and see what happens.
Grigory and Andrew have the same opinion. So, once upon a time, they went to the shop and bought n packets with inflatable balloons, where i-th of them has exactly a_i balloons inside.
They want to divide the balloons among themselves. In addition, there are several conditions to hold:
* Do not rip the packets (both Grigory and Andrew should get unbroken packets);
* Distribute all packets (every packet should be given to someone);
* Give both Grigory and Andrew at least one packet;
* To provide more fun, the total number of balloons in Grigory's packets should not be equal to the total number of balloons in Andrew's packets.
Help them to divide the balloons or determine that it's impossible under these conditions.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 10) — the number of packets with balloons.
The second line contains n integers: a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000) — the number of balloons inside the corresponding packet.
Output
If it's impossible to divide the balloons satisfying the conditions above, print -1.
Otherwise, print an integer k — the number of packets to give to Grigory followed by k distinct integers from 1 to n — the indices of those. The order of packets doesn't matter.
If there are multiple ways to divide balloons, output any of them.
Examples
Input
3
1 2 1
Output
2
1 2
Input
2
5 5
Output
-1
Input
1
10
Output
-1
Note
In the first test Grigory gets 3 balloons in total while Andrey gets 1.
In the second test there's only one way to divide the packets which leads to equal numbers of balloons.
In the third test one of the boys won't get a packet at all.
Submitted Solution:
```
n = int(input())
A = list(map(int, input().split()))
if n == 1:
print(-1)
elif len(A) == 2:
if A[0] != A[1]:
print(1)
print(A[0])
else:
print(-1)
else:
if sum(A) - A[n - 1] != A[:n-1]:
print(1)
print(A[n - 1])
else:
print(2)
print(A[n-1], A[n-2])
```
No
| 13,106 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are quite a lot of ways to have fun with inflatable balloons. For example, you can fill them with water and see what happens.
Grigory and Andrew have the same opinion. So, once upon a time, they went to the shop and bought n packets with inflatable balloons, where i-th of them has exactly a_i balloons inside.
They want to divide the balloons among themselves. In addition, there are several conditions to hold:
* Do not rip the packets (both Grigory and Andrew should get unbroken packets);
* Distribute all packets (every packet should be given to someone);
* Give both Grigory and Andrew at least one packet;
* To provide more fun, the total number of balloons in Grigory's packets should not be equal to the total number of balloons in Andrew's packets.
Help them to divide the balloons or determine that it's impossible under these conditions.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 10) — the number of packets with balloons.
The second line contains n integers: a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000) — the number of balloons inside the corresponding packet.
Output
If it's impossible to divide the balloons satisfying the conditions above, print -1.
Otherwise, print an integer k — the number of packets to give to Grigory followed by k distinct integers from 1 to n — the indices of those. The order of packets doesn't matter.
If there are multiple ways to divide balloons, output any of them.
Examples
Input
3
1 2 1
Output
2
1 2
Input
2
5 5
Output
-1
Input
1
10
Output
-1
Note
In the first test Grigory gets 3 balloons in total while Andrey gets 1.
In the second test there's only one way to divide the packets which leads to equal numbers of balloons.
In the third test one of the boys won't get a packet at all.
Submitted Solution:
```
n = int(input())
ar = input().split()
mi = ar.index(min(ar))
print("-1" if n == 2 and ar[0] == ar[1] else "1 " + str(mi))
```
No
| 13,107 |
Provide a correct Python 3 solution for this coding contest problem.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
"Correct Solution:
```
input()
a=[int(i) for i in input().split()]
ans=1
if 0 in a:
print(0)
exit()
for i in a:
ans*=i
if ans>10**18:
print(-1)
exit()
print(ans)
```
| 13,108 |
Provide a correct Python 3 solution for this coding contest problem.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
"Correct Solution:
```
N=int(input())
ans=1
A=list(map(int, input().split()))
for i in range(N):
ans=ans*A[i]
if ans>10**18 or ans<0:
ans=-1
print(ans)
```
| 13,109 |
Provide a correct Python 3 solution for this coding contest problem.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
"Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
a.sort()
t=1
for i in a:
t*=i
if t>10**18:
t=-1
break
print(t)
```
| 13,110 |
Provide a correct Python 3 solution for this coding contest problem.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
"Correct Solution:
```
n,*a=map(int,open(0).read().split())
a.sort()
ans=1
for ai in a:
ans*=ai
if ans>10**18:
print(-1)
exit()
print(ans)
```
| 13,111 |
Provide a correct Python 3 solution for this coding contest problem.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
"Correct Solution:
```
a,b=open(0);c=1;
for i in sorted(b.split()):
c*=int(i)
if c>10**18:c=-1;break
print(c)
```
| 13,112 |
Provide a correct Python 3 solution for this coding contest problem.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
"Correct Solution:
```
n = int(input())
a = map(int, input().split())
a = sorted(a)
s = 1
for x in a:
s *= x;
if s > 1e18:
print(-1)
exit()
print(s)
```
| 13,113 |
Provide a correct Python 3 solution for this coding contest problem.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
"Correct Solution:
```
N=int(input())
A=[*map(int,input().split())]
a=1
if 0 in A:
a=0
else:
while A:
a*=A.pop()
if a>10**18:
a=-1
break
print(a)
```
| 13,114 |
Provide a correct Python 3 solution for this coding contest problem.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
"Correct Solution:
```
n,*a=map(int,open(0).read().split())
a.sort()
ans=1
for i in a:
ans*=i
if ans>1e18:
print(-1)
exit()
print(ans)
```
| 13,115 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
Submitted Solution:
```
n=int(input())
A=list(map(int,input().split()))
A.sort()
ans = 1
for i in A:
ans *= i
if ans>10**18:
print(-1)
exit()
print(ans)
```
Yes
| 13,116 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
Submitted Solution:
```
N = int(input())
ans = 1
for a in sorted(input().split()):
ans *= int(a)
if ans > 10**18:
print(-1)
exit()
print(ans)
```
Yes
| 13,117 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
Submitted Solution:
```
x=int(input())
s=list(map(int,input().split()))
s.sort()
res=1
for n in s:
res*=n
if res>1e18:
res=-1
print(-1)
exit(0)
print(res)
```
Yes
| 13,118 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
Submitted Solution:
```
n=int(input())
A=list(map(int,input().split()))
s=1
if 0 in A:
s=0
else:
for a in A:
s*=a
if s>10**18:
s=-1
break
print(s)
```
Yes
| 13,119 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
Submitted Solution:
```
N = int(input())
As = list(map(lambda x: int(x), input().split(" ")))
LIMIT = 10**18
result = 1
for a in As:
result *= a
if result > LIMIT:
result = -1
break
print(result)
```
No
| 13,120 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
Submitted Solution:
```
N=int(input())
L=list(map(int,input().split()))
A=1
if 0 in L:
print(0)
for i in range(N):
A=A*L[i]
if 10**18<A:
print(-1)
exit()
print(A)
```
No
| 13,121 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
Submitted Solution:
```
n=int(input())
A=list(map(int,input().split()))
if 0 in a:
print(0)
else:
a=1
for i in A:
a=a*i
if a>1000000000000000000:
print(-1)
else:
print(a)
```
No
| 13,122 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given N integers A_1, ..., A_N, compute A_1 \times ... \times A_N.
However, if the result exceeds 10^{18}, print `-1` instead.
Constraints
* 2 \leq N \leq 10^5
* 0 \leq A_i \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 ... A_N
Output
Print the value A_1 \times ... \times A_N as an integer, or `-1` if the value exceeds 10^{18}.
Examples
Input
2
1000000000 1000000000
Output
1000000000000000000
Input
3
101 9901 999999000001
Output
-1
Input
31
4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0
Output
0
Submitted Solution:
```
N=int(input())
A=input().split()
answer=1
for i in range(N):
answer=answer*int(A[i])
if answer>1*10**18:
print(-1)
else:
print(answer)
```
No
| 13,123 |
Provide a correct Python 3 solution for this coding contest problem.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
"Correct Solution:
```
H, N, *AB = map(int, open(0).read().split())
dp = [0] * (H + max(AB[::2]))
for i in range(1, len(dp)):
dp[i] = min(dp[i - a] + b for a, b in zip(*[iter(AB)] * 2))
print(min(dp[H:]))
```
| 13,124 |
Provide a correct Python 3 solution for this coding contest problem.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
"Correct Solution:
```
H,N = map(int,input().split())
AB = [list(map(int,input().split())) for _ in range(N)]
maxA = max(a for a,b in AB)
dp = [0]*(H+maxA)
for i in range(1,H + maxA):
dp[i] = min(dp[i-a]+b for a,b in AB)
print(dp[H])
```
| 13,125 |
Provide a correct Python 3 solution for this coding contest problem.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
"Correct Solution:
```
h, n = map(int, input().split())
AB = [list(map(int, input().split())) for _ in range(n)]
dp = [1 << 31] * (h + 10**4)
dp[0] = 0
for i in range(h):
for a, b in AB:
dp[i + a] = min(dp[i + a], dp[i] + b)
print(min(dp[h:]))
```
| 13,126 |
Provide a correct Python 3 solution for this coding contest problem.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
"Correct Solution:
```
h,n=map(int,input().split())
dp=[10**10 for i in range(h+1)]
dp[0]=0
for i in range(n):
x,y=map(int,input().split())
for j in range(h+1):
nj=min(h,j+x)
dp[nj]=min(dp[nj],dp[j]+y)
print(dp[h])
```
| 13,127 |
Provide a correct Python 3 solution for this coding contest problem.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
"Correct Solution:
```
H,N = map(int,input().split())
MAXH = H+10000
DP = [float("inf")]*MAXH
DP[0] = 0
for i in range(N):
a,b = map(int,input().split())
for j in range(MAXH-a):
if j>H+a:break
DP[j+a] = min(DP[j+a],DP[j]+b)
print(min(DP[H:]))
```
| 13,128 |
Provide a correct Python 3 solution for this coding contest problem.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
"Correct Solution:
```
h,n = map(int, input().split())
magics = [tuple(map(int, input().split())) for _ in range(n)]
max_a = sorted(magics, key=lambda x: x[0], reverse=True)[0][0]
dp = [0]*(h+max_a)
for i in range(1, h+max_a):
dp[i] = min(dp[i-a]+b for a,b in magics)
print(min(dp[h:]))
```
| 13,129 |
Provide a correct Python 3 solution for this coding contest problem.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
"Correct Solution:
```
h, n = map(int, input().split())
ab = [list(map(int, input().split())) for i in range(n)]
table = [float("inf")] * (h + 10000)
table[0] = 0
for a, b in ab:
for i in range(h):
table[i+a] = min(table[i+a], table[i] + b)
print(min(table[h:]))
```
| 13,130 |
Provide a correct Python 3 solution for this coding contest problem.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
"Correct Solution:
```
h, n = map(int, input().split())
magics = [list(map(int, input().split())) for _ in range(n)]
max_damage = max(a for a, b in magics)
dp = [0] * (h + max_damage)
for i in range(1, h + max_damage):
dp[i] = min(dp[i - a] + b for a, b in magics)
print(dp[h])
```
| 13,131 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
Submitted Solution:
```
h, n = list(map(int, input().split()))
ab = [list(map(int, input().split())) for _ in range(n)]
dp = [0] * (h+max(a for a,b in ab))
for i in range(1, len(dp)):
dp[i] = min(dp[i-a]+b for a, b in ab)
print(min(dp[h:]))
```
Yes
| 13,132 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
Submitted Solution:
```
h,n=map(int,input().split())
l=[list(map(int,input().split())) for _ in range(n)]
dp=[10**9]*(h+max(l)[0])
dp[0]=0
for i in range(1,len(dp)):
for a,b in l:
if i-a>=0:
dp[i]=min(dp[i],dp[i-a]+b)
print(min(dp[h:]))
```
Yes
| 13,133 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
Submitted Solution:
```
h,n = list(map(int, input().split()))
ab = [list(map(int, input().split())) for _ in range(n)]
dp = [10**10]*(h+1)
dp[h] = 0
for i in range(h,0,-1):
for j in ab:
tmp = max(0,i-j[0])
dp[tmp] = min(dp[tmp], dp[i]+j[1])
print(dp[0])
```
Yes
| 13,134 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
Submitted Solution:
```
from operator import itemgetter
h,n=map(int,input().split())
ab=[list(map(int,input().split())) for i in range(n)]
infi=10**9
dp=[infi]*2*10**4
dp[0]=0
for a,b in ab:
for i in range(h):
if dp[i]!=infi:
dp[i+a]=min(dp[i+a],dp[i]+b)
print(min(dp[h:]))
```
Yes
| 13,135 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
Submitted Solution:
```
inf = 1000000000
dp = [inf] * 20000
h, n = map(int, input().split())
dp[0] = 0
for j in range(n):
a, b = map(int, input().split())
for i in range(h + 1):
dp[i + a] = min(dp[i + a], dp[i] + b)
print(min(dp[h:]))
```
No
| 13,136 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
Submitted Solution:
```
h,n=map(int,input().split())
ab=[list(map(int,input().split())) for _ in range(n)]
max_a=max(a for a,_ in ab)
dp = [0] * (h+max_a)
for i in range(0,h+max_a):
if i==0:
d[i]=0
else:
dp[i]=min(dp[i-a]+b for a,b in ab)
print(min(dp[h:]))
```
No
| 13,137 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
Submitted Solution:
```
h,n,*L=map(int,open(0).read().split())
dp=[float('inf')]*(h+10100)
dp[0]=0
for a,b in zip(*[iter(L)]*2):
for i in range(h):
t=dp[i]+b
if t<dp[i+a]:
dp[i+a]=dp[i]+b
print(min(dp[h:]))
```
No
| 13,138 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ibis is fighting with a monster.
The health of the monster is H.
Ibis can cast N kinds of spells. Casting the i-th spell decreases the monster's health by A_i, at the cost of B_i Magic Points.
The same spell can be cast multiple times. There is no way other than spells to decrease the monster's health.
Ibis wins when the health of the monster becomes 0 or below.
Find the minimum total Magic Points that have to be consumed before winning.
Constraints
* 1 \leq H \leq 10^4
* 1 \leq N \leq 10^3
* 1 \leq A_i \leq 10^4
* 1 \leq B_i \leq 10^4
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H N
A_1 B_1
:
A_N B_N
Output
Print the minimum total Magic Points that have to be consumed before winning.
Examples
Input
9 3
8 3
4 2
2 1
Output
4
Input
100 6
1 1
2 3
3 9
4 27
5 81
6 243
Output
100
Input
9999 10
540 7550
691 9680
700 9790
510 7150
415 5818
551 7712
587 8227
619 8671
588 8228
176 2461
Output
139815
Submitted Solution:
```
H,N=map(int, input().split())
AB = [list(map(int,input().split())) for i in range(N)]
dp=[10**8]*(H+1)
dp[0]=0
for i in range(1,H+1):
for ab in AB:
dp[i]=min(dp[max(0,i-ab[0])] + ab[1], dp[i])
print(dp[-1])
```
No
| 13,139 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
"Correct Solution:
```
n=int(input())
h=list(map(int,input().split()))
res=[]
t=0
for i in range(1,n):
if h[i]<=h[i-1]:
t+=1
else:
res.append(t)
t=0
res.append(t)
print(max(res))
```
| 13,140 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
"Correct Solution:
```
n = int(input())
a = list(map(int,input().split()))
b=[]
x=0
for i in range(n-1):
if a[i]>=a[i+1]:
x+=1
else:
b.append(x)
x=0
b.append(x)
print(max(b))
```
| 13,141 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
"Correct Solution:
```
n=int(input())
h=list(map(int,input().split()))
l=[0]*n
for i in range(1,n):
if h[i]<=h[i-1]:
l[i]=1+l[i-1]
print(max(l))
```
| 13,142 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
"Correct Solution:
```
N = int(input())
H = [int(_) for _ in input().split()]
num = [0] * N
for i in range(N-2, -1, -1):
if H[i] >= H[i+1]:
num[i] = num[i+1]+1
print(max(num))
```
| 13,143 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
"Correct Solution:
```
N = int(input())
H = list(map(int,input().split()))
a =[0]*(N+1)
for i in range(N-1,0,-1):
if H[i]<=H[i-1]:
a[i] = a[i+1]+1
print(max(a))
```
| 13,144 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
"Correct Solution:
```
n,a=input(),list(map(int,input().split()))
ans,now,cnt=0,10**20,0
for i in a:
if i>now:
cnt=0
cnt+=1
now=i
ans=max(ans,cnt)
print(ans-1)
```
| 13,145 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
"Correct Solution:
```
n=int(input())
a=[int(i) for i in input().split()]
m=0
c=0
for i in range(n-1):
if a[i]>=a[i+1]:
c+=1
else:
c=0
if c>m:
m=c
print(m)
```
| 13,146 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
"Correct Solution:
```
N=int(input())
H=list(map(int,input().split()))
a=b=c=0
for i in range(N):
if H[i]<=a:
a=H[i]
b+=1
if b>=c:
c=b
else:
a=H[i]
b=0
print(c)
```
| 13,147 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
Submitted Solution:
```
N = int(input())
H= list(map(int, input().split()))
res = [0]
for i in range(N-1):
if H[i+1]<=H[i]:
res[-1]+=1
else:
res.append(0)
print(max(res))
```
Yes
| 13,148 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
Submitted Solution:
```
n,h=open(0);a=b=c=0
for i in map(int,h.split()):c=(b>=i)*-~c;b=i;a=max(a,c)
print(a)
```
Yes
| 13,149 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
Submitted Solution:
```
n=int(input())
h=[int(i) for i in input().split()]
j=0
k=0
for i in range(1,len(h)):
if h[i-1]>=h[i]:
j+=1
else:
k=max(k,j)
j=0
k=max(k,j)
print(k)
```
Yes
| 13,150 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
Submitted Solution:
```
n=int(input())
H=list(map(int,input().split()))
res=0
cnt=0
for i in range(n-1):
if H[i]>=H[i+1]:
cnt += 1
else:
cnt = 0
res=max(res,cnt)
print(res)
```
Yes
| 13,151 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
Submitted Solution:
```
n = int(input())
h = list(map(int, input().split()))
a = 0
move = []
for i in range(n-1):
if h[i] >= h[i+1]:
a += 1
else:
move.append(a)
a = 0
print(max(move))
```
No
| 13,152 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
Submitted Solution:
```
n = int(input())
h = list(map(int,input().split()))
h.append(10**10)
counter = []
for i in range(n):
cnt = 0
for j in range(i,n):
if h[j]>=h[j+1]:
cnt +=1
else:
counter.append(cnt)
break
ans = max(counter)
print(ans)
```
No
| 13,153 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
Submitted Solution:
```
def main():
# n,k = map(int,input().split())
n = int(input())
# s = str(input())
h = list(map(int,input().split()))
# l = [list(map(int, input().split())) for _ in range(n)]
# s = list(s)
ans = 0
dp = [0] * n
if n == 1:
print(0)
if n == 2:
if h[0] >= h[1]:
print(1)
else:
print(0)
else:
if h[0] >= h[1]:
dp[0] = 1
for i in range(1,n-1):
if h[i] >= h[i+1]:
dp[i] = dp[i-1] + 1
else:
dp[i] = 0
print(max(dp))
if __name__ == '__main__':
main()
```
No
| 13,154 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares arranged in a row from left to right.
The height of the i-th square from the left is H_i.
You will land on a square of your choice, then repeat moving to the adjacent square on the right as long as the height of the next square is not greater than that of the current square.
Find the maximum number of times you can move.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq H_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
H_1 H_2 ... H_N
Output
Print the maximum number of times you can move.
Examples
Input
5
10 4 8 7 3
Output
2
Input
7
4 4 5 6 6 5 5
Output
3
Input
4
1 2 3 4
Output
0
Submitted Solution:
```
N = int(input())
H = input().split()
Move = 0
tmp = 0
for i in range(N-1):
if int(H[i+1]) > int(H[i]):
tmp = 0
if Move < tmp:
Move = tmp
else:
tmp += 1
print(H[i],H[i+1])
if Move < tmp:
Move = tmp
print(Move)
```
No
| 13,155 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a tree T with N vertices and an undirected graph G with N vertices and M edges. The vertices of each graph are numbered 1 to N. The i-th of the N-1 edges in T connects Vertex a_i and Vertex b_i, and the j-th of the M edges in G connects Vertex c_j and Vertex d_j.
Consider adding edges to G by repeatedly performing the following operation:
* Choose three integers a, b and c such that G has an edge connecting Vertex a and b and an edge connecting Vertex b and c but not an edge connecting Vertex a and c. If there is a simple path in T that contains all three of Vertex a, b and c in some order, add an edge in G connecting Vertex a and c.
Print the number of edges in G when no more edge can be added. It can be shown that this number does not depend on the choices made in the operation.
Constraints
* 2 \leq N \leq 2000
* 1 \leq M \leq 2000
* 1 \leq a_i, b_i \leq N
* a_i \neq b_i
* 1 \leq c_j, d_j \leq N
* c_j \neq d_j
* G does not contain multiple edges.
* T is a tree.
Input
Input is given from Standard Input in the following format:
N M
a_1 b_1
:
a_{N-1} b_{N-1}
c_1 d_1
:
c_M d_M
Output
Print the final number of edges in G.
Examples
Input
5 3
1 2
1 3
3 4
1 5
5 4
2 5
1 5
Output
6
Input
7 5
1 5
1 4
1 7
1 2
2 6
6 3
2 5
1 3
1 6
4 6
4 7
Output
11
Input
13 11
6 13
1 2
5 1
8 4
9 7
12 2
10 11
1 9
13 7
13 11
8 10
3 8
4 13
8 12
4 7
2 3
5 11
1 4
2 11
8 10
3 5
6 9
4 10
Output
27
Submitted Solution:
```
print("5")
```
No
| 13,156 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a tree T with N vertices and an undirected graph G with N vertices and M edges. The vertices of each graph are numbered 1 to N. The i-th of the N-1 edges in T connects Vertex a_i and Vertex b_i, and the j-th of the M edges in G connects Vertex c_j and Vertex d_j.
Consider adding edges to G by repeatedly performing the following operation:
* Choose three integers a, b and c such that G has an edge connecting Vertex a and b and an edge connecting Vertex b and c but not an edge connecting Vertex a and c. If there is a simple path in T that contains all three of Vertex a, b and c in some order, add an edge in G connecting Vertex a and c.
Print the number of edges in G when no more edge can be added. It can be shown that this number does not depend on the choices made in the operation.
Constraints
* 2 \leq N \leq 2000
* 1 \leq M \leq 2000
* 1 \leq a_i, b_i \leq N
* a_i \neq b_i
* 1 \leq c_j, d_j \leq N
* c_j \neq d_j
* G does not contain multiple edges.
* T is a tree.
Input
Input is given from Standard Input in the following format:
N M
a_1 b_1
:
a_{N-1} b_{N-1}
c_1 d_1
:
c_M d_M
Output
Print the final number of edges in G.
Examples
Input
5 3
1 2
1 3
3 4
1 5
5 4
2 5
1 5
Output
6
Input
7 5
1 5
1 4
1 7
1 2
2 6
6 3
2 5
1 3
1 6
4 6
4 7
Output
11
Input
13 11
6 13
1 2
5 1
8 4
9 7
12 2
10 11
1 9
13 7
13 11
8 10
3 8
4 13
8 12
4 7
2 3
5 11
1 4
2 11
8 10
3 5
6 9
4 10
Output
27
Submitted Solution:
```
import queue
SIZE = 2000
vec = [[] for _ in range(SIZE)]
par = [[-1] * SIZE for _ in range(SIZE)]
id_ = [[-1] * SIZE for _ in range(SIZE)]
ans = 0
def dfs(v: int, p: int, rt: int):
par[rt][v] = p
for to in vec[v]:
if to == p:
continue
dfs(to, v, rt)
def dfs2(v: int, p: int, b: int):
global ans
if id_[b][v] == v:
ans += 1
b = v
for to in vec[v]:
if to == p:
continue
dfs2(to, v, b)
def add(a: int, b: int):
if id_[a][b] == b or id_[b][a] == a:
return
if id_[a][b] != -1:
add(id_[a][b], b)
return
if id_[b][a] != -1:
add(id_[b][a], a)
return
id_[a][b] = b
id_[b][a] = a
nxt = []
que = queue.Queue()
que.put(b)
while not que.empty():
v = que.get()
for to in vec[v]:
if to == par[a][v]:
continue
if id_[a][to] != -1:
nxt.append((to, b))
else:
id_[a][to] = b
que.put(to)
que.put(a)
while not que.empty():
v = que.get()
for to in vec[v]:
if to == par[b][v]:
continue
if id_[b][to] != -1:
nxt.append((to, a))
else:
id_[b][to] = a
que.put(to)
for u, v in nxt:
add(u, v)
def adding_edges(N: int, M: int, T: list, G: list)->int:
global ans
for a, b in T:
vec[a-1].append(b-1)
vec[b-1].append(a-1)
for i in range(N):
dfs(i, -1, i)
for c, d in G:
add(c-1, d-1)
for i in range(N):
for to in vec[i]:
dfs2(to, i, i)
return ans//2
if __name__ == "__main__":
N = 0
M = 0
N, M = map(int, input().split())
T = [tuple(int(s) for s in input().split()) for _ in range(N-1)]
G = [tuple(int(s) for s in input().split()) for _ in range(M)]
ans = adding_edges(N, M, T, G)
print(ans)
```
No
| 13,157 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a tree T with N vertices and an undirected graph G with N vertices and M edges. The vertices of each graph are numbered 1 to N. The i-th of the N-1 edges in T connects Vertex a_i and Vertex b_i, and the j-th of the M edges in G connects Vertex c_j and Vertex d_j.
Consider adding edges to G by repeatedly performing the following operation:
* Choose three integers a, b and c such that G has an edge connecting Vertex a and b and an edge connecting Vertex b and c but not an edge connecting Vertex a and c. If there is a simple path in T that contains all three of Vertex a, b and c in some order, add an edge in G connecting Vertex a and c.
Print the number of edges in G when no more edge can be added. It can be shown that this number does not depend on the choices made in the operation.
Constraints
* 2 \leq N \leq 2000
* 1 \leq M \leq 2000
* 1 \leq a_i, b_i \leq N
* a_i \neq b_i
* 1 \leq c_j, d_j \leq N
* c_j \neq d_j
* G does not contain multiple edges.
* T is a tree.
Input
Input is given from Standard Input in the following format:
N M
a_1 b_1
:
a_{N-1} b_{N-1}
c_1 d_1
:
c_M d_M
Output
Print the final number of edges in G.
Examples
Input
5 3
1 2
1 3
3 4
1 5
5 4
2 5
1 5
Output
6
Input
7 5
1 5
1 4
1 7
1 2
2 6
6 3
2 5
1 3
1 6
4 6
4 7
Output
11
Input
13 11
6 13
1 2
5 1
8 4
9 7
12 2
10 11
1 9
13 7
13 11
8 10
3 8
4 13
8 12
4 7
2 3
5 11
1 4
2 11
8 10
3 5
6 9
4 10
Output
27
Submitted Solution:
```
from collections import deque
a=[]
def bfs(maze, visited, sy, sx):
queue = deque([[sy, sx]])
visited[sy][sx] = 0
while queue:
y, x = queue.popleft()
if queue == False:
return visited[y][x]
for j, k in ([1, 0], [-1, 0], [0, 1], [0, -1]):
new_y, new_x = y+j, x+k
if maze[new_y][new_x] == "." and \
visited[new_y][new_x] == -1:
visited[new_y][new_x] = visited[y][x] + 1
queue.append([new_y, new_x])
if __name__ == "__main__":
R, C = map(int, input().split())
for h in range(R):
k=input()
a.append(k)
for p in k:
p="#"
maze = [input() for i in range(R)]
visited = [[-1]*C for j in range(R)]
print(bfs(maze, visited, sy, sx))
```
No
| 13,158 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a tree T with N vertices and an undirected graph G with N vertices and M edges. The vertices of each graph are numbered 1 to N. The i-th of the N-1 edges in T connects Vertex a_i and Vertex b_i, and the j-th of the M edges in G connects Vertex c_j and Vertex d_j.
Consider adding edges to G by repeatedly performing the following operation:
* Choose three integers a, b and c such that G has an edge connecting Vertex a and b and an edge connecting Vertex b and c but not an edge connecting Vertex a and c. If there is a simple path in T that contains all three of Vertex a, b and c in some order, add an edge in G connecting Vertex a and c.
Print the number of edges in G when no more edge can be added. It can be shown that this number does not depend on the choices made in the operation.
Constraints
* 2 \leq N \leq 2000
* 1 \leq M \leq 2000
* 1 \leq a_i, b_i \leq N
* a_i \neq b_i
* 1 \leq c_j, d_j \leq N
* c_j \neq d_j
* G does not contain multiple edges.
* T is a tree.
Input
Input is given from Standard Input in the following format:
N M
a_1 b_1
:
a_{N-1} b_{N-1}
c_1 d_1
:
c_M d_M
Output
Print the final number of edges in G.
Examples
Input
5 3
1 2
1 3
3 4
1 5
5 4
2 5
1 5
Output
6
Input
7 5
1 5
1 4
1 7
1 2
2 6
6 3
2 5
1 3
1 6
4 6
4 7
Output
11
Input
13 11
6 13
1 2
5 1
8 4
9 7
12 2
10 11
1 9
13 7
13 11
8 10
3 8
4 13
8 12
4 7
2 3
5 11
1 4
2 11
8 10
3 5
6 9
4 10
Output
27
Submitted Solution:
```
# no sub撤退をしないという覚悟
print('nan')
```
No
| 13,159 |
Provide a correct Python 3 solution for this coding contest problem.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
"Correct Solution:
```
N = int(input())
*A, = map(int, input().split())
def check(K):
st = []
for i, a in enumerate(A):
#print(K, i, st, a)
while st and a < st[-1][0]:
st.pop()
u = i > 0 and A[i-1] >= A[i]
if not st:
st.append([a, u])
continue
l = st[-1]
if l[0] == a:
l[1] += 1
while st and l[1] == K:
st.pop(); a -= 1
if a == 0:
return 0
if not st:
st.append([a, 1])
break
l = st[-1]
if l[0] == a:
l[1] += 1
else:
st.append([a, 1])
break
#print(l, st)
else:
st.append([a, u])
#print(st)
return 1
ok = 1
for i in range(N-1):
if not A[i] < A[i+1]:
ok = 0
if ok:
print(1)
exit(0)
left = 1; right = N+1
while left+1 < right:
mid = (left + right) // 2
if check(mid):
right = mid
else:
left = mid
print(right)
```
| 13,160 |
Provide a correct Python 3 solution for this coding contest problem.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
"Correct Solution:
```
import sys
stdin = sys.stdin
sys.setrecursionlimit(10**5)
def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x)-1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())
def shave(stack:list, nex:int, prv:int):
res = prv-nex
while res > 0:
if res >= stack[-1][1]:
_,y = stack.pop()
res -= y
else:
stack[-1][1] -= res
res = 0
def normalize(stack: list):
if stack[-1][0] == stack[-2][0]:
stack[-2][1] += stack[-1][1]
stack.pop()
def add(stack:list):
if stack[-1][1] == 1:
stack[-1][0] += 1
else:
stack[-1][1] -= 1
stack.append([stack[-1][0]+1, 1])
def kuriagari(stack:list):
_, y = stack.pop()
add(stack)
normalize(stack)
stack.append([1,y])
def check(a:list, upto:int):
stack = [[0,0]]
for i in range(n):
if a[i+1] > a[i]:
stack.append([1, a[i+1]-a[i]])
normalize(stack)
else:
shave(stack, a[i+1], a[i])
if stack[-1][0] == upto and stack[-1][1] == a[i+1]:
return False
elif stack[-1][0] == upto:
kuriagari(stack)
else:
add(stack)
normalize(stack)
return True
def binsearch(a:list):
low = 0
high = 10**9+1
while high-low > 1:
mid = (high+low) // 2
if check(a, mid):
high = mid
else:
low = mid
return high
n = ni()
a = [0] + list(li())
ans = binsearch(a)
print(ans)
```
| 13,161 |
Provide a correct Python 3 solution for this coding contest problem.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
ok, ng = n, 0
while ok-ng > 1:
x = (ok+ng)//2
#d = defaultdict(int)
d = dict()
last = 0
valid = True
if x == 1:
for i in range(n-1):
if a[i] >= a[i+1]:
valid = False
break
if valid:
ok = x
else:
ng = x
continue
for i in range(n-1):
dels = []
if a[i] < a[i+1]:
last = a[i+1]
continue
j = a[i+1]
for k in d.keys():
if j < k:
dels.append(k)
while j > 0:
if j in d and d[j] == x-1:
#d[j] = 0
dels.append(j)
j -= 1
else:
break
if j in d:
d[j] += 1
else:
d[j] = 1
for k in dels:
del d[k]
if 0 in d:
valid = False
break
last = j
if valid:
ok = x
else:
ng = x
print(ok)
```
| 13,162 |
Provide a correct Python 3 solution for this coding contest problem.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
"Correct Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
A = [int(x) for x in input().split()]
A.append(1)
B = [A[0]]
B_cnt = [1]
for i,(x,y) in enumerate(zip(A[:-1],A[1:])):
if x < y and y < A[i+2]:
continue
if x == y:
B_cnt[-1] += 1
else:
B.append(y)
B_cnt.append(1)
def test(x):
digit = [0]
cnt = [0]
for a,a_cnt in zip(B,B_cnt):
if digit[-1] < a:
digit.append(a)
cnt.append(a_cnt)
continue
if digit[-1] == a:
cnt[-1] += a_cnt
continue
while True:
# 繰り上がり処理をしながら左に戻る
if digit[-1] <= a:
break
n = digit.pop()
k = cnt.pop()
if k <= x:
continue
if digit[-1] == n-1:
cnt[-1] += (k-1)//x
else:
digit.append(n-1)
cnt.append((k-1)//x + 1)
if digit[-1] == a:
cnt[-1] += a_cnt
else:
digit.append(a)
cnt.append(1+a_cnt)
return cnt[1] <= x+1
if all(x<y for x,y in zip(A[:-2],A[1:-1])):
print(1)
exit()
left = 1 # 無理
right = 10 # 可能?
while not test(right):
left *= 10
right *= 10
right = min(right,N)
while right > left + 1:
mid = (left+right)//2
if test(mid):
right = mid
else:
left = mid
answer = right
print(answer)
```
| 13,163 |
Provide a correct Python 3 solution for this coding contest problem.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
"Correct Solution:
```
N = int(input())
A = [int(a) for a in input().split()]
def chk(k):
if k == 1:
for i in range(1, N):
if A[i] <= A[i-1]: return 0
return 1
X = [(0, 0)]
def add(x, y):
if x <= 0: return 0
if x > X[-1][0]:
X.append((x, 0 if x == y else 1))
elif x == X[-1][0]:
if X[-1][1] + 1 < k:
X[-1] = (X[-1][0], X[-1][1] + 1)
else:
if add(x-1, y) == 0: return 0
else:
while X[-1][0] > x:
X.pop()
if x > X[-1][0]:
X.append((x, 1))
elif x == X[-1][0]:
if X[-1][1] + 1 < k:
X[-1] = (X[-1][0], X[-1][1] + 1)
else:
if add(x-1, y) == 0: return 0
if X[-1][0] < y: X.append((y, 0))
return 1
for a in A:
if add(a, a) == 0: return 0
return 1
l, r = 0, 1 << 18
while r - l > 1:
m = (l + r) // 2
if chk(m):
r = m
else:
l = m
print(r)
```
| 13,164 |
Provide a correct Python 3 solution for this coding contest problem.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
"Correct Solution:
```
def is_possible(x, A):
current = {}
length = 0
for a in A:
if a <= length:
if x == 1:
return False
current = {k: current[k] for k in current if k < a}
i = a - 1
if i not in current:
current[i] = 0
current[i] += 1
while i in current and current[i] >= x:
if i == 0:
return False
if (i-1) not in current:
current[i-1] = 0
current[i-1] += 1
del current[i]
i -= 1
length = a
return True
def main():
N = int(input())
A = list(map(int, input().split()))
left = 1
right = N
while left < right:
center = (left + right) // 2
if is_possible(center, A):
right = center
else:
left = center + 1
print(left)
if __name__ == "__main__":
main()
```
| 13,165 |
Provide a correct Python 3 solution for this coding contest problem.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
"Correct Solution:
```
N = int(input())
A_raw = list(map(int, input().split()))
flg = 1
prev = 0
A = []
for i in range(N):
if A_raw[i] <= prev:
flg = 0
prev = A_raw[i]
if A_raw[i] <= 50:
A.append(A_raw[i])
if flg:
print(1)
exit()
N = len(A)
if N <= 1:
print(2)
exit()
ok = N
ng = 1
mid = (ok + ng) // 2
while ok - ng > 1:
ng_flg = 0
word = [1] * A[0]
for i in range(1, N):
if A[i] > A[i-1]:
word.extend([1] * (A[i] - A[i-1]))
else:
word_prev = word[:A[i]]
k = A[i] - 1
while True:
if k == -1:
ng_flg = 1
break
if word_prev[k] != mid:
word_prev[k] += 1
word = word_prev
break
else:
word_prev[k] = 1
k -= 1
if ng_flg == 1:
break
if not ng_flg:
ok = mid
else:
ng = mid
mid = (ok + ng) // 2
print(ok)
```
| 13,166 |
Provide a correct Python 3 solution for this coding contest problem.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
"Correct Solution:
```
def solve(aaa):
l = 1
r = 200000
while l < r:
m = (l + r) // 2
if check(m, aaa):
r = m
else:
l = m + 1
return r
def check(d, aaa):
if d == 1:
return all(a1 < a2 for a1, a2 in zip(aaa, aaa[1:]))
l = 0
word = [[0, 0]]
for a in aaa:
if l >= a:
if not carry(d, word, a):
return False
l = a
return True
def carry(d, word, i):
while word[-1][0] > i:
word.pop()
while word[-1] == [i, d]:
word.pop()
i -= 1
if i == 0:
return False
if word[-1][0] == i:
word[-1][1] += 1
else:
word.append([i, 2])
return True
n = int(input())
aaa = list(map(int, input().split()))
print(solve(aaa))
```
| 13,167 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
Submitted Solution:
```
def main():
import heapq
n = int(input())
a = list(map(int, input().split()))
for i in range(n-1):
if a[i] >= a[i+1]:
break
else:
print(1)
return
h = []
heapq.heapify(h)
kind = 1
length = 0
d = dict()
for i in a:
if length >= i:
while h:
hh = -heapq.heappop(h)
if hh > i:
d.pop(hh)
else:
heapq.heappush(h, -hh)
break
for j in range(i, 0, -1):
if j not in d:
d[j] = 2
heapq.heappush(h, -j)
kind = max(kind, 2)
while h:
hh = -heapq.heappop(h)
if hh > j:
d.pop(hh)
else:
heapq.heappush(h, -hh)
break
break
else:
if d[j] < kind:
d[j] += 1
while h:
hh = -heapq.heappop(h)
if hh > j:
d.pop(hh)
else:
heapq.heappush(h, -hh)
break
break
else:
d[i] += 1
kind += 1
length = i
def value(kind):
length = 0
d = dict()
for i in a:
if length >= i:
del_list = []
for j in d:
if j > i:
del_list.append(j)
for j in del_list:
d.pop(j)
for j in range(i, 0, -1):
if j not in d:
d[j] = 2
break
else:
if d[j] < kind:
d[j] += 1
break
else:
d.pop(j)
else:
return False
length = i
return True
def b_search(ok, ng, value):
while abs(ok-ng) > 1:
mid = (ok+ng)//2
if value(mid):
ok = mid
else:
ng = mid
return ok
print(b_search(kind, max(1, kind-30), value))
main()
```
Yes
| 13,168 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
Submitted Solution:
```
import random
input()
A = [int(_) for _ in input().split()]
A = [A[0]] + [j for i, j in zip(A, A[1:]) if i >= j]
N = len(A)
def cut(array, index):
if index < 1:
return []
if index <= array[0][0]:
return [(index, array[0][1])]
for _ in range(len(array)-1, 0, -1):
if array[_ - 1][0] < index:
return array[:_] + [(index, array[_][1])]
def is_possible(K):
dp = [(A[0], 0)]
for a in A[1:]:
if a <= dp[-1][0]:
dp = cut(dp, a)
else:
dp += [(a, 0)]
is_added = False
for j in range(len(dp) - 1, -1, -1):
if dp[j][1] < K - 1:
dp = cut(dp, dp[j][0] - 1) + [(dp[j][0], dp[j][1] + 1)]
if dp[-1][0] < a:
dp += [(a, 0)]
is_added = True
break
if not is_added:
return False
return True
def bis(x, y):
if y == x + 1:
return y
elif is_possible((x + y) // 2):
return bis(x, (x + y) // 2)
else:
return bis((x + y) // 2, y)
print(bis(0, N))
```
Yes
| 13,169 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
Submitted Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
A = list(map(int, input().split()))
# import random
# N = 10**5
# A = [random.randrange(1,10**9+1) for _ in range(N)]
# import time
def main():
l = 0
r = N
while r-l > 1:
m = (r+l)//2
ok = True
if m == 1:
pre = -1
for a in A:
if pre >= a:
ok = False
break
pre = a
else:
dp = {}
needreset = 10**15
exception = set()
pre = -1
for a in A:
ind = a
for _ in range(40):
# 修正
if needreset >= ind or ind in exception:
if not ind in dp:
dp[ind] = 0 if pre < a else 1
else:
dp[ind] = 0 if pre < a else 1
exception.add(ind)
# たす
if dp[ind] < m:
dp[ind] += 1
break
elif ind == 1:
ok = False
break
else:
# 繰り上がり
dp[ind] = 1
ind -= 1
if not ok: break
# 更新
if pre > a:
needreset = a
exception = set()
pre = a
if ok:
r = m
else:
l = m
print(r)
if __name__ == "__main__":
#dt = time.time()
main()
#print(time.time()-dt)
```
Yes
| 13,170 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
Submitted Solution:
```
import bisect
from collections import deque
"""
def pl(d,k):
now = d
ind = bisect.bisect_left(dlis,d)
while ind > 0:
dic[dlis[ind]] += 1
if dic[dlis[ind]] // k == 0:
dic[dlis[ind]] = 0
else:
break
ind -= 1
def able(k):
ndep = A[0]
for i in range(len(dlis)):
dic[dlis[i]] = 0
for i in range(N-1):
i += 1
if ndep < A[i]:
dic[A[i]] = 0
ndep = A[i]
else:
ndep = A[i]
pl(ndep,k)
print (dic,k)
if dic[dlis[0]] < k:
return True
else:
return False
"""
def updiv(a,b):
if a % b == 0:
return a // b
else:
return a // b + 1
def able(k):
nq = deque([0])
num = deque([A[0]])
for i in range(N-1):
i += 1
if A[i] > A[i-1]:
if nq[-1] == 0:
num[-1] += A[i] - A[i-1]
else:
nq.append(0)
num.append(A[i] - A[i-1])
else:
if A[i] < A[i-1]:
ds = A[i-1] - A[i]
while len(num) > 0 and ds >= num[-1]:
nq.pop()
ds -= num[-1]
num.pop()
if len(num) == 0:
return False
num[-1] -= ds
now = 0
while len(nq) > 0 and nq[-1] == k-1:
now += num[-1]
nq.pop()
num.pop()
if len(nq) == 0:
return False
if num[-1] == 1:
nq[-1] += 1
else:
num[-1] -= 1
nq.append(nq[-1] + 1)
num.append(1)
if now > 0:
nq.append(0)
num.append(now)
while len(nq) > 1 and nq[-1] == nq[-2]:
num[-2] += num[-1]
nq.pop()
num.pop()
#print (k,A[i])
#print (nq)
#print (num)
return True
N = int(input())
A = list(map(int,input().split()))
A.append(1)
l = 0
r = N
while r - l != 1 :
m = (l + r) // 2
if able(m):
r = m
else:
l = m
print (r)
```
Yes
| 13,171 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
Submitted Solution:
```
from collections import defaultdict
from copy import copy
n = int(input())
a = list(map(int, input().split()))
ok, ng = n, 0
while ok-ng > 1:
x = (ok+ng)//2
d = defaultdict(int)
last = 0
valid = True
if x == 1:
for i in range(n-1):
if a[i] >= a[i+1]:
valid = False
break
if valid:
ok = x
else:
ng = x
continue
for i in range(n-1):
if a[i] > a[i+1]:
if a[i+1] > last:
d[a[i+1]] = 1
else:
j = a[i+1]
while d[j] == x-1 and j > 0:
del d[j]
j -= 1
d[j] += 1
last = a[i+1]
elif a[i] == a[i+1]:
j = a[i+1]
while d[j] == x-1 and j > 0:
del d[j]
j -= 1
d[j] += 1
last = a[i+1]
e = copy(d)
for k in d.keys():
if k > last:
del e[k]
d = copy(e)
#if x < 5:
#print(x, last, d)
if d[0] > 0:
valid = False
break
if valid:
ok = x
else:
ng = x
print(ok)
```
No
| 13,172 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
Submitted Solution:
```
N = int(input())
A = list(map(int, input().split()))
ans = 0
for i in range(N - 1):
if A[i] > A[i + 1]:
ans += 1
print(ans)
```
No
| 13,173 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
Submitted Solution:
```
def main():
n = int(input())
a = list(map(int, input().split()))
for i in range(n-1):
if a[i] >= a[i+1]:
break
else:
print(1)
return
def value(kind):
length = 0
d = []
for i in a:
if length >= i:
while d:
j, k = d[-1]
if j > i:
d.pop()
else:
break
l = len(d)-1
if d:
jj, k = d[-1]
else:
jj, k = -1, -1
for j in range(i, 0, -1):
if jj != j:
d.append([j, 2])
kind = max(kind, 2)
break
else:
if k < kind:
d[l][1] += 1
for jjj in range(l+1, len(d)):
d.pop()
else:
l -= 1
else:
return False
length = i
return True
def b_search(ok, ng, value):
while abs(ok-ng) > 1:
mid = (ok+ng)//2
if value(mid):
ok = mid
else:
ng = mid
return ok
print(b_search(n, 1, value))
main()
```
No
| 13,174 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.
At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?
Constraints
* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the minimum possible number of different characters contained in the strings.
Examples
Input
3
3 2 1
Output
2
Input
5
2 3 2 1 2
Output
2
Submitted Solution:
```
N = int(input())
A = [int(i) for i in input().split()]
def f(al, X):
def g(stack, X):
if not any(stack):
stack.append(-1)
return
l = stack.pop()
if l >= X:
g(stack, X)
stack.append(1)
else:
stack.append(l + 1)
st = []
s = 0
for t in al:
d = t - s
if d > 0:
st.extend([1] * d)
else:
for _ in range(-d):
st.pop()
g(st, X)
if st[0] < 0:
return False
s = t
return True
max_N = N
min_N = len([i for i in A if i == 1])
b_max_N = 0
b_min_N = 0
while max_N != min_N:
nx = (max_N + min_N) // 2
if f(A, nx):
max_N = nx
else:
min_N = nx
if b_max_N == max_N and b_min_N == min_N:
break
b_max_N = max_N
b_min_N = min_N
print(max_N)
```
No
| 13,175 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Find the number of the possible tuples of sequences (A_0,A_1,...,A_N) that satisfy all of the following conditions, modulo M:
* For every i (0\leq i\leq N), A_i is a sequence of length i consisting of integers between 1 and K (inclusive);
* For every i (1\leq i\leq N), A_{i-1} is a subsequence of A_i, that is, there exists 1\leq x_i\leq i such that the removal of the x_i-th element of A_i would result in a sequence equal to A_{i-1};
* For every i (1\leq i\leq N), A_i is lexicographically larger than A_{i-1}.
Constraints
* 1 \leq N,K \leq 300
* 2 \leq M \leq 10^9
* N, K and M are integers.
Input
Input is given from Standard Input in the following format:
N K M
Output
Print the number of the possible tuples of sequences (A_0,A_1,...,A_N), modulo M.
Examples
Input
2 2 100
Output
5
Input
4 3 999999999
Output
358
Input
150 150 998244353
Output
186248260
Submitted Solution:
```
#include <bits/stdc++.h>
using namespace std;
vector<vector<int64_t> > get_combination(int N, int M) {
vector<vector<int64_t> > mat(N + 1, vector<int64_t>(N + 1));
for (int i = 0; i <= N; i++) {
for (int j = 0; j <= i; j++) {
if (j == 0 || j == i)
mat[i][j] = 1;
else
mat[i][j] = mat[i - 1][j - 1] + mat[i - 1][j];
mat[i][j] %= M;
}
}
return (mat);
}
int main() {
int N, K, M;
cin >> N >> K >> M;
auto C = get_combination(N, M);
int dp[302][302] = {{}};
for (int i = 0; i <= K; i++) {
dp[1][i] = 1;
}
for (int i = 2; i <= N + 1; i++) {
int sub[302] = {};
for (int j = K - 1; j >= 0; j--) {
for (int k = 0; k < i; k++) {
sub[k] += dp[k][j + 1];
sub[k] %= M;
}
for (int k = 1; k <= i; k++) {
dp[i][j] += 1LL * dp[i - k][j] * C[i - 2][k - 1] % M * sub[k] % M;
dp[i][j] %= M;
}
}
}
cout << dp[N + 1][0] << endl;
}
```
No
| 13,176 |
Provide a correct Python 3 solution for this coding contest problem.
Ringo Kingdom Congress is voting on a bill.
N members are present, and the i-th member (1 ≤ i ≤ N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.
After all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.
In order for the bill to pass, at least how many members must be in favor of it?
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ P ≤ 100
* 1 ≤ w_i ≤ 10^9
* 1 ≤ b_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N P
w_1 b_1
w_2 b_2
:
w_N b_N
Output
Print the minimum number of members in favor of the bill required for passage.
Examples
Input
4 75
1 1
1 1
1 1
1 1
Output
3
Input
4 75
1 1
1 1
1 1
100 1
Output
1
Input
5 60
6 3
5 9
3 4
7 8
4 7
Output
3
"Correct Solution:
```
n, p = map(int, input().split())
e = [tuple(map(int, input().split())) for _ in range(n)]
# e = [(w,b), ...]
e2 = sorted(((100 - p) * w + p * b for w, b in e), reverse=True)
rest = p * sum(b for _, b in e)
cur = 0
while rest > 0 and cur < n:
rest -= e2[cur]
cur += 1
print(cur)
```
| 13,177 |
Provide a correct Python 3 solution for this coding contest problem.
Ringo Kingdom Congress is voting on a bill.
N members are present, and the i-th member (1 ≤ i ≤ N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.
After all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.
In order for the bill to pass, at least how many members must be in favor of it?
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ P ≤ 100
* 1 ≤ w_i ≤ 10^9
* 1 ≤ b_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N P
w_1 b_1
w_2 b_2
:
w_N b_N
Output
Print the minimum number of members in favor of the bill required for passage.
Examples
Input
4 75
1 1
1 1
1 1
1 1
Output
3
Input
4 75
1 1
1 1
1 1
100 1
Output
1
Input
5 60
6 3
5 9
3 4
7 8
4 7
Output
3
"Correct Solution:
```
n, p = map(int, input().split())
w, b = [], []
for _ in range(n):
ww, bb = map(int, input().split())
w.append(ww)
b.append(bb)
s = []
for ww, bb in zip(w, b):
s.append((100 - p) * ww + p * bb)
s.sort(reverse=True)
score = -sum(b) * p
cnt = 0
while score < 0:
score += s[cnt]
cnt += 1
print(cnt)
# (100-p)*w-p*b>=0
```
| 13,178 |
Provide a correct Python 3 solution for this coding contest problem.
Ringo Kingdom Congress is voting on a bill.
N members are present, and the i-th member (1 ≤ i ≤ N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.
After all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.
In order for the bill to pass, at least how many members must be in favor of it?
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ P ≤ 100
* 1 ≤ w_i ≤ 10^9
* 1 ≤ b_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N P
w_1 b_1
w_2 b_2
:
w_N b_N
Output
Print the minimum number of members in favor of the bill required for passage.
Examples
Input
4 75
1 1
1 1
1 1
1 1
Output
3
Input
4 75
1 1
1 1
1 1
100 1
Output
1
Input
5 60
6 3
5 9
3 4
7 8
4 7
Output
3
"Correct Solution:
```
n,p=map(int,input().split())
l=[]
for i in range(n):
l.append(list(map(int,input().split())))
l.sort(key=lambda x:-(x[0]*(100-p)+x[1]*p))
z=0
for i in range(n):
z+=-l[i][1]*p
i=0
while z<0:
z+=l[i][0]*(100-p)+l[i][1]*p
i+=1
print(i)
```
| 13,179 |
Provide a correct Python 3 solution for this coding contest problem.
Ringo Kingdom Congress is voting on a bill.
N members are present, and the i-th member (1 ≤ i ≤ N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.
After all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.
In order for the bill to pass, at least how many members must be in favor of it?
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ P ≤ 100
* 1 ≤ w_i ≤ 10^9
* 1 ≤ b_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N P
w_1 b_1
w_2 b_2
:
w_N b_N
Output
Print the minimum number of members in favor of the bill required for passage.
Examples
Input
4 75
1 1
1 1
1 1
1 1
Output
3
Input
4 75
1 1
1 1
1 1
100 1
Output
1
Input
5 60
6 3
5 9
3 4
7 8
4 7
Output
3
"Correct Solution:
```
N, P = map(int, input().split())
B = 0
Q = []
for i in range(N):
w, b = map(int, input().split())
B += b
Q.append((100 - P)*w + P*b)
Q.sort()
s = 0
for i in range(N):
s += Q[-i-1]
if B*P <= s:
print(i+1)
break
```
| 13,180 |
Provide a correct Python 3 solution for this coding contest problem.
Ringo Kingdom Congress is voting on a bill.
N members are present, and the i-th member (1 ≤ i ≤ N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.
After all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.
In order for the bill to pass, at least how many members must be in favor of it?
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ P ≤ 100
* 1 ≤ w_i ≤ 10^9
* 1 ≤ b_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N P
w_1 b_1
w_2 b_2
:
w_N b_N
Output
Print the minimum number of members in favor of the bill required for passage.
Examples
Input
4 75
1 1
1 1
1 1
1 1
Output
3
Input
4 75
1 1
1 1
1 1
100 1
Output
1
Input
5 60
6 3
5 9
3 4
7 8
4 7
Output
3
"Correct Solution:
```
N,P=[int(i) for i in input().split()]
wb=[[int(j) for j in input().split()] for i in range(N)]
xs = [(100-P)*w+P*b for w,b in wb]
xs.sort()
xs.reverse()
score=0
for i in range(N):
score-=P*wb[i][1]
for i in range(N):
score+=xs[i]
if score>=0:
print(i+1)
break
```
| 13,181 |
Provide a correct Python 3 solution for this coding contest problem.
Ringo Kingdom Congress is voting on a bill.
N members are present, and the i-th member (1 ≤ i ≤ N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.
After all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.
In order for the bill to pass, at least how many members must be in favor of it?
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ P ≤ 100
* 1 ≤ w_i ≤ 10^9
* 1 ≤ b_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N P
w_1 b_1
w_2 b_2
:
w_N b_N
Output
Print the minimum number of members in favor of the bill required for passage.
Examples
Input
4 75
1 1
1 1
1 1
1 1
Output
3
Input
4 75
1 1
1 1
1 1
100 1
Output
1
Input
5 60
6 3
5 9
3 4
7 8
4 7
Output
3
"Correct Solution:
```
from itertools import accumulate
def solve(l, r):
if l > r:
return l
m = (l + r) // 2
w, b = whites[m], blues[m]
if w * 100 // (w + b) < p:
l = m + 1
else:
r = m - 1
return solve(l, r)
n, p = map(int, input().split())
wbs = [tuple(map(int, input().split())) for _ in range(n)]
ass = [(w * (100 - p) + b * p, i) for i, (w, b) in enumerate(wbs)]
ass.sort(reverse=True)
whites = list(accumulate(wbs[i][0] for _, i in ass))
blues = [wbs[i][1] for _, i in ass[1:]]
blues = list(reversed(list(accumulate(reversed(blues))))) + [0]
# print(list(whites))
# print(list(blues))
print(solve(0, n - 1) + 1)
```
| 13,182 |
Provide a correct Python 3 solution for this coding contest problem.
Ringo Kingdom Congress is voting on a bill.
N members are present, and the i-th member (1 ≤ i ≤ N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.
After all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.
In order for the bill to pass, at least how many members must be in favor of it?
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ P ≤ 100
* 1 ≤ w_i ≤ 10^9
* 1 ≤ b_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N P
w_1 b_1
w_2 b_2
:
w_N b_N
Output
Print the minimum number of members in favor of the bill required for passage.
Examples
Input
4 75
1 1
1 1
1 1
1 1
Output
3
Input
4 75
1 1
1 1
1 1
100 1
Output
1
Input
5 60
6 3
5 9
3 4
7 8
4 7
Output
3
"Correct Solution:
```
N, P = map(int, input().split())
xs = []
value = 0
for _ in range(N):
w, b = map(int, input().split())
xs.append((100-P)*w+P*b)
value -= P*b
xs.sort(reverse=True)
for i, x in enumerate(xs, 1):
value += x
if value >= 0:
print(i)
break
```
| 13,183 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ringo Kingdom Congress is voting on a bill.
N members are present, and the i-th member (1 ≤ i ≤ N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.
After all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.
In order for the bill to pass, at least how many members must be in favor of it?
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ P ≤ 100
* 1 ≤ w_i ≤ 10^9
* 1 ≤ b_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N P
w_1 b_1
w_2 b_2
:
w_N b_N
Output
Print the minimum number of members in favor of the bill required for passage.
Examples
Input
4 75
1 1
1 1
1 1
1 1
Output
3
Input
4 75
1 1
1 1
1 1
100 1
Output
1
Input
5 60
6 3
5 9
3 4
7 8
4 7
Output
3
Submitted Solution:
```
from itertools import accumulate
def solve(l, r):
if l > r:
return l
m = (l + r) // 2
w, b = whites[m], blues[m]
if w * 100 // (w + b) < p:
l = m + 1
else:
r = m - 1
return solve(l, r)
n, p = map(int, input().split())
wbs = [tuple(map(int, input().split())) for _ in range(n)]
ass = [(sum(t), i) for i, t in enumerate(wbs)]
ass.sort(reverse=True)
whites = list(accumulate(wbs[i][0] for s, i in ass))
blues = [wbs[i][1] for s, i in ass[1:]]
blues = list(reversed(list(accumulate(reversed(blues))))) + [0]
# print(list(whites))
# print(list(blues))
print(solve(0, n - 1) + 1)
```
No
| 13,184 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Ringo Kingdom Congress is voting on a bill.
N members are present, and the i-th member (1 ≤ i ≤ N) has w_i white ballots and b_i blue ballots. Each member i will put all the w_i white ballots into the box if he/she is in favor of the bill, and put all the b_i blue ballots into the box if he/she is not in favor of the bill. No other action is allowed. For example, a member must not forfeit voting, or put only a part of his/her white ballots or a part of his/her blue ballots into the box.
After all the members vote, if at least P percent of the ballots in the box is white, the bill is passed; if less than P percent of the ballots is white, the bill is rejected.
In order for the bill to pass, at least how many members must be in favor of it?
Constraints
* 1 ≤ N ≤ 10^5
* 1 ≤ P ≤ 100
* 1 ≤ w_i ≤ 10^9
* 1 ≤ b_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N P
w_1 b_1
w_2 b_2
:
w_N b_N
Output
Print the minimum number of members in favor of the bill required for passage.
Examples
Input
4 75
1 1
1 1
1 1
1 1
Output
3
Input
4 75
1 1
1 1
1 1
100 1
Output
1
Input
5 60
6 3
5 9
3 4
7 8
4 7
Output
3
Submitted Solution:
```
from itertools import accumulate
def solve(l, r):
if l > r:
return l
m = (l + r) // 2
w, b = whites[m], blues[m]
if w * 100 // (w + b) < p:
l = m + 1
else:
r = m - 1
return solve(l, r)
n, p = map(int, input().split())
wbs = [tuple(map(int, input().split())) for _ in range(n)]
ass = [(sum(t), t[0], i) for i, t in enumerate(wbs)]
ass.sort(reverse=True)
whites = list(accumulate(wbs[i][0] for s, t, i in ass))
blues = [wbs[i][1] for s, t, i in ass[1:]]
blues = list(reversed(list(accumulate(reversed(blues))))) + [0]
# print(list(whites))
# print(list(blues))
print(solve(0, n - 1) + 1)
```
No
| 13,185 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N(N+1)/2 dots arranged to form an equilateral triangle whose sides consist of N dots, as shown below. The j-th dot from the left in the i-th row from the top is denoted by (i, j) (1 \leq i \leq N, 1 \leq j \leq i). Also, we will call (i+1, j) immediately lower-left to (i, j), and (i+1, j+1) immediately lower-right to (i, j).
<image>
Takahashi is drawing M polygonal lines L_1, L_2, ..., L_M by connecting these dots. Each L_i starts at (1, 1), and visits the dot that is immediately lower-left or lower-right to the current dots N-1 times. More formally, there exist X_{i,1}, ..., X_{i,N} such that:
* L_i connects the N points (1, X_{i,1}), (2, X_{i,2}), ..., (N, X_{i,N}), in this order.
* For each j=1, 2, ..., N-1, either X_{i,j+1} = X_{i,j} or X_{i,j+1} = X_{i,j}+1 holds.
Takahashi would like to draw these lines so that no part of L_{i+1} is to the left of L_{i}. That is, for each j=1, 2, ..., N, X_{1,j} \leq X_{2,j} \leq ... \leq X_{M,j} must hold.
Additionally, there are K conditions on the shape of the lines that must be followed. The i-th condition is denoted by (A_i, B_i, C_i), which means:
* If C_i=0, L_{A_i} must visit the immediately lower-left dot for the B_i-th move.
* If C_i=1, L_{A_i} must visit the immediately lower-right dot for the B_i-th move.
That is, X_{A_i, {B_i}+1} = X_{A_i, B_i} + C_i must hold.
In how many ways can Takahashi draw M polygonal lines? Find the count modulo 1000000007.
Constraints
* 1 \leq N \leq 20
* 1 \leq M \leq 20
* 0 \leq K \leq (N-1)M
* 1 \leq A_i \leq M
* 1 \leq B_i \leq N-1
* C_i = 0 or 1
* No pair appears more than once as (A_i, B_i).
Input
Input is given from Standard Input in the following format:
N M K
A_1 B_1 C_1
A_2 B_2 C_2
:
A_K B_K C_K
Output
Print the number of ways for Takahashi to draw M polygonal lines, modulo 1000000007.
Examples
Input
3 2 1
1 2 0
Output
6
Input
3 2 2
1 1 1
2 1 0
Output
0
Input
5 4 2
1 3 1
4 2 0
Output
172
Input
20 20 0
Output
881396682
Submitted Solution:
```
print(881396682)
```
No
| 13,186 |
Provide a correct Python 3 solution for this coding contest problem.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
"Correct Solution:
```
def main():
S = input()
print("%s %s" % (S[:4], S[4:]))
if __name__ == "__main__":
main()
```
| 13,187 |
Provide a correct Python 3 solution for this coding contest problem.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
"Correct Solution:
```
s=input()
a=s[:4]
b=s[4:]
print(a+" "+b)
```
| 13,188 |
Provide a correct Python 3 solution for this coding contest problem.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
"Correct Solution:
```
s = input()
a = s[:4]
b = s[4:]
print(a + ' ' + b)
```
| 13,189 |
Provide a correct Python 3 solution for this coding contest problem.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
"Correct Solution:
```
# 2019/12/21
s=input()
print(s[:4]+' '+s[4:])
```
| 13,190 |
Provide a correct Python 3 solution for this coding contest problem.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
"Correct Solution:
```
a = input()
ans = a[:4] + ' ' + a[4:]
print(ans)
```
| 13,191 |
Provide a correct Python 3 solution for this coding contest problem.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
"Correct Solution:
```
S= input()
print(S[:4]+" "+S[-8:])
```
| 13,192 |
Provide a correct Python 3 solution for this coding contest problem.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
"Correct Solution:
```
s = list(input())
for i in range(12):
if i!=3:
print(s[i], end="")
else:
print(s[i]+" ", end="")
print()
```
| 13,193 |
Provide a correct Python 3 solution for this coding contest problem.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
"Correct Solution:
```
s = str(input())
print(s[0:4]+" "+s[4:])
```
| 13,194 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
Submitted Solution:
```
N=input()
print(N[0:4]+" "+N[4:16])
```
Yes
| 13,195 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
Submitted Solution:
```
def main():
s=input()
print(s[0:4],s[4:],sep=' ')
main()
```
Yes
| 13,196 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
Submitted Solution:
```
s=input()
for i, j in enumerate(s):
if i==4:
print(" ", end="")
print(j, end="")
print("")
```
Yes
| 13,197 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
Submitted Solution:
```
code_festival = input()
code = code_festival[:4]
festival = code_festival[4:]
code_festival = code + " " + festival
print (code_festival)
```
Yes
| 13,198 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This contest is `CODE FESTIVAL`. However, Mr. Takahashi always writes it `CODEFESTIVAL`, omitting the single space between `CODE` and `FESTIVAL`.
So he has decided to make a program that puts the single space he omitted.
You are given a string s with 12 letters. Output the string putting a single space between the first 4 letters and last 8 letters in the string s.
Constraints
* s contains exactly 12 letters.
* All letters in s are uppercase English letters.
Input
The input is given from Standard Input in the following format:
s
Output
Print the string putting a single space between the first 4 letters and last 8 letters in the string s. Put a line break at the end.
Examples
Input
CODEFESTIVAL
Output
CODE FESTIVAL
Input
POSTGRADUATE
Output
POST GRADUATE
Input
ABCDEFGHIJKL
Output
ABCD EFGHIJKL
Submitted Solution:
```
N = int(input())
usa = list(map(int, input().split()))
print (usa[0])
for i, j in enumerate(usa):
if(usa[j]-1 == i):
count+=1
if(i >= N/2):
break
print (count)
```
No
| 13,199 |
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