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:
def gen_primes(upper_bound):
    upper_bound += 1
    t = [0] * (upper_bound)
    primes = [2]
    for i in range(3, upper_bound, 2):
        if t[i]: continue
        primes.append(i)
        for j in range(i + i, upper_bound, i): t[j] = 1
    return primes

def main():
    tprimes = set([p * p for p in gen_primes(int(1E6))])
    _ = input()
    x = list(map(int, input().split()))
    print('\n'.join('YES' if i in tprimes else 'NO' for i in x))

if __name__ == '__main__':
    main()