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;
int main() {
  long long int i, j, n;
  long long int x;
  long long int m = 1000001;
  vector<bool> primes(1000001, true);
  set<long long int> st;
  primes[0] = primes[1] = false;
  for (i = 2; i * i <= m; i++) {
    if (primes[i]) {
      for (j = i; i * j <= m; j++) {
        primes[i * j] = false;
      }
    }
  }
  for (i = 2; i <= m; i++) {
    if (primes[i]) st.insert(i * i);
  }
  cin >> n;
  while (n--) {
    cin >> x;
    if (st.find(x) != st.end())
      cout << "YES";
    else
      cout << "NO";
    cout << endl;
  }
  return 0;
}