## LENGFACT - Factorial length

no tags

Given integer n, print length of n! (which is factorial of n).

### Input

The first line of the standard input contains one integer t (t < 10001) which is the number of test cases.

In each of the next t lines there is number n (0 <= n <= 5*10^9).

### Output

For each test, print the length of n! (which is factorial of n).

### Example

`Input:3110100Output:17158`

## Code Examples

### #1 Code Example with Python Programming

```Code - Python Programming```

``````import math

T = int(input())
for _ in range(T):
N = int(input())
if N < 2:
print(1)
else:
print(math.floor((math.log(2 * math.pi * N) / 2 + \
N * (math.log(N) - 1)) / math.log(10) \
) + 1)``````
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Input

cmd
3
1
10
100

Output

cmd
1
7
158

### #2 Code Example with C++ Programming

```Code - C++ Programming```

``````#include<iostream7gt;
#include<cmath>
using namespace std;
int main()
{
int t;
cin>>t;
double n;
double pi = 2*acos(0);
long long int len,l;

while(t-->0)
{
cin>>n;
if(n==0.00||n==1.00)l=1;

else{
l=(((log(2.00*pi*n)/2.00)+(n*(log(n)-1.00)))/log(10.0))+1;
}

cout<<l<<endl;
}
return 0;
}``````
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Input

cmd
3
1
10
100

Output

cmd
1
7
158