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() {
  ios::sync_with_stdio(false);
  vector<long long int> a;
  long long int p[168] = {
      2,   3,   5,   7,   11,  13,  17,  19,  23,  29,  31,  37,  41,  43,
      47,  53,  59,  61,  67,  71,  73,  79,  83,  89,  97,  101, 103, 107,
      109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181,
      191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
      269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
      353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433,
      439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521,
      523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613,
      617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
      709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
      811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887,
      907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997};
  for (long long int i = 2; i <= 1000006; i++) {
    bool y = 0;
    for (long long int j = 0; j < 168 && p[j] * p[j] <= i; j++) {
      if (i % p[j] == 0) {
        y = 1;
        break;
      }
    }
    if (y == 0) a.push_back(i * i);
  }
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    long long int z;
    cin >> z;
    if (binary_search(a.begin(), a.end(), z) == true)
      cout << "YES\n";
    else
      cout << "NO\n";
  }
}