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;
const int N = 100010;
template <typename T>
inline void read(T& x) {
  x = 0;
  char q;
  bool f = 1;
  while (!isdigit(q = getchar()))
    if (q == '-') f = 0;
  while (isdigit(q)) {
    x = (x << 1) + (x << 3) + (q ^ 48);
    q = getchar();
  }
  x = f ? x : -x;
}
template <typename T>
inline void print(T x) {
  if (x < 0) {
    x = -x;
    putchar('-');
  }
  if (x > 9) print(x / 10);
  putchar(x % 10 + '0');
}
int n;
long long a;
int main() {
  read(n);
  while (n--) {
    read(a);
    if (a == 1) {
      puts("NO");
      continue;
    }
    if (a == 4) {
      puts("YES");
      continue;
    }
    if (a % 2 == 0) {
      puts("NO");
      continue;
    }
    long long q = sqrt(a);
    if (q * q != a) {
      puts("NO");
      continue;
    }
    bool f = 1;
    int qq = sqrt(q);
    for (int i = 3; i <= qq; i += 2)
      if (q % i == 0) {
        f = 0;
        break;
      }
    if (f == 0)
      puts("NO");
    else
      puts("YES");
  }
  return 0;
}