SGU 113

113. Nearly prime numbers

time limit per test: 0.25 sec.
memory limit per test: 4096 KB

Nearly prime number is an integer positive number for which it is possible to find such primes P₁ and P₂ that given number is equal to P₁*P₂. There is given a sequence on N integer positive numbers, you are to write a program that prints “Yes” if given number is nearly prime and “No” otherwise.

Input

Input file consists of N+1 numbers. First is positive integer N (1£N£10). Next N numbers followed by N. Each number is not greater than 10⁹. All numbers separated by whitespace(s).

Output

Write a line in output file for each number of given sequence. Write “Yes” in it if given number is nearly prime and “No” in other case.

Sample Input

1

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

int n;

bool judge(int x) {
        int sum = 0;
        int t;
        for(int i = 2; i * i <= x; i++) {
                if(x % i == 0 ) {
                        sum++;
                        t = i;

                }
        }

        return sum == 1 && ((x / t == t) || x / t % t != 0) ;
}
int main()
{

    scanf("%d",&n);

    for(int i = 1; i <= n; i++) {
            int ch;
            scanf("%d",&ch);
            if(judge(ch)) printf("Yes
");
            else printf("No
");
    }
    return 0;
}

6

Sample Output

Yes

 易知，我们要寻找的数除1 与自身外其他的因子数必然不超过2，假设有两个因子，则其中一个因子必然不能整除另一个因子。