Leftmost Digit

Description

Given a positive integer N, you should output the leftmost digit of N^N.

 

Input

The input contains several test cases. The first line of the input is a single integer T which is the number of test cases. T test cases follow.
Each test case contains a single positive integer N(1<=N<=1,000,000,000).

 

Output

For each test case, you should output the leftmost digit of N^N.

 

Sample Input

2 3 4

 

Sample Output

2 2

Hint

 In the first case, 3 * 3 * 3 = 27, so the leftmost digit is 2. In the second case, 4 * 4 * 4 * 4 = 256, so the leftmost digit is 2. 

题意：给一个整数N，要求输出N的N次方最左边的数；
分析：
令 N=X^X;
　两边同时取对数 则 log10（N）=X*log10（X）；
　同时 X^X 也可以表示成 A*(10^k) 科学计数法表示    
　　　　 A的整数部分即是X^X的最高位
两式合并得   log10（A）+k=X*log10（X）；
log10（A）小于1 即是右式的小数部分 k是右式的整数部分
此时只需通过右式算出k即可解得A

#include<cstdio>
#include<cstring>
#include<iostream>
#include<cmath>
using namespace std;

int main()
{
    int T;
    cin>>T;
    while(T--)
    {
        double A,n;
        long long k;
        cin>>n;
        A=n*log10(n);
        A-=(long long)A;
        k=pow(10.0,A);
        cout<<k<<endl;
    }
}