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 PYTHON3):

Solution:
from math import sqrt
from sys import stdin, stdout
n = int(stdin.readline())
v = [int(t) for t in stdin.readline().split()]
for x in v:
    if x == 1:
        ans = "NO"
    else:
        r = int(sqrt(x))
        if r * r != x:
            ans = "NO"
        else:
            x = r
            r = int(sqrt(x))
            ans = "YES"
            for i in range(2, r + 1):
                if x % i == 0:
                    ans = "NO"
                    break
    stdout.write(ans)
    stdout.write('\n')