学步园

Description

Input

Output

Sample Input

2
10
20

Sample Output

7
19

//此题必须用公式才能AC,数据规模太大了
//Stirling公式:    n! = ((2*pi*n)^(1/2))*((n/e)^n); 前提是n > 3
//由此可以导出lg(n!) = (lg(2*pi)+lg(n))/2 + n*(lg(n)-lg(e)); 
#include<iostream>
#include<cmath>

using namespace std;

int main()
{
	int test,n;
	long long int s;
	const long double c1 = 0.798179868358; //lg(2*pi)
	const long double c2 = 0.434294481903; //lg(e)
	long double c3;
	cin >> test;
	while(--test+1)
	{
		cin >> n;
		c3 = log10((double)n);
		s = 1;
		if(n > 3)
		{
			s = (c3 + c1)/2 + n * (c3 - c2) + 1;
			cout << s << endl;
		}
		else
			cout << 1 << endl; 
	}
	return 0;
}