Problem Description

In many applications very large integers numbers arerequired. Some of these applications are using keys for secure transmission ofdata, encryption, etc. In this problem you are given a number, you have todetermine the number of digits in the factorial of the number.

Input

Input consists of several lines of integer numbers. Thefirst line contains an integer n, which is the number of cases to be tested,followed by n lines, one integer 1 ≤ n ≤107 on each line.

Output

The output contains the number of digits in the factorialof the integers appearing in the input.

Sample Input

2
10
20

 
Sample Output

7
19

 1 #include <stdio.h> 2 #include <math.h> 3    4 int main(){ 5     int n; 6     int number; 7     double result; 8     int i; 9   10     scanf("%d",&n);11   12     while(n--){13         result=0;14   15         scanf("%d",&number);16   17         for(i=1;i<=number;i++){18             result+=log10(i);19   20         }21   22         printf("%.0lf\n",ceil(result));23     }24   25     return 0;26 }

Big Number