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

                 }
         }

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

     scanf("%d",&n);

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

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。