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 PYTHON):

Solution:
import math

MAX_N = 1001000
primes = [True] * MAX_N
primes[1] = False

def gen_prime():
    for i in range(2, MAX_N):
        if primes[i]:
            for j in range(i * 2, MAX_N, i):
                primes[j] = False

def is_ok(x):
    s = int(math.sqrt(x))
    if s**2 != int(x):
        return False
    return primes[s]


if __name__ == '__main__':
    n = input()
    nums = map(int, raw_input().split())
    gen_prime()
    for i in range(0, n):
        print (is_ok(nums[i]) and ['YES'] or ['NO'])[0]