Problem: We know that prime numbers are positive integers that have exactly two distinct positive divisors. Similarly, we'll call a positive integer t Т-prime, if t has exactly three distinct positive divisors.

You are given an array of n positive integers. For each of them determine whether it is Т-prime or not.

Input

The first line contains a single positive integer, n (1 ≤ n ≤ 105), showing how many numbers are in the array. The next line contains n space-separated integers xi (1 ≤ xi ≤ 1012).

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is advised to use the cin, cout streams or the %I64d specifier.

Output

Print n lines: the i-th line should contain "YES" (without the quotes), if number xi is Т-prime, and "NO" (without the quotes), if it isn't.

Examples

Input

3
4 5 6


Output

YES
NO
NO

Note

The given test has three numbers. The first number 4 has exactly three divisors — 1, 2 and 4, thus the answer for this number is "YES". The second number 5 has two divisors (1 and 5), and the third number 6 has four divisors (1, 2, 3, 6), hence the answer for them is "NO".

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long n;
bool prime[1000100];
int main() {
  memset(prime, 1, sizeof(prime));
  for (long long i = 3; i < 1000100; i++)
    if (i % 2 == 0) prime[i] = 0;
  long long t = sqrt(1000100 * 1.0);
  for (long long i = 2; i <= t; i++) {
    if (prime[i]) {
      for (long long j = 2 * i; j < 1000100; j += i) {
        prime[j] = 0;
      }
    }
  }
  cin >> n;
  long long x;
  for (long long i = 0; i < n; i++) {
    scanf("%I64d", &x);
    if (x == 1 || x == 0) {
      cout << "NO\n";
      continue;
    }
    long long shuzi = sqrt(1.0 * x);
    if (sqrt(1.0 * x) - shuzi > 0) {
      cout << "NO\n";
      continue;
    }
    if (prime[shuzi]) {
      cout << "YES\n";
    } else {
      cout << "NO\n";
    }
  }
}