大数阶乘的位数

import java.util.*;
import java.math.*;
class Main
{
    public static void main(String args[])
    {
        Scanner cin=new Scanner(System.in);
        int i,n,m,des=0;
        double sum,e=2.7182818284590452354,PI=3.141592653589793239;
        while(cin.hasNext())
        {
            n=cin.nextInt();
            while(n-->0)
            {
                m=cin.nextInt();
                if(m<100000)
                {
                    for(sum=0,i=1;i<=m;i++)
                    {
                        sum+=Math.log10(i);
                    }
                }
                else
                {
                    sum=Math.log10(Math.sqrt(2*PI*m))+m*Math.log10(m/e);
                }
                des=(int)sum;
                if(des<=sum)des++;
                System.out.println(des);
            }
        }
    }
}