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 main():
    l = ['NO'] * int(input())
    sieve = bytearray(b'\0\0\1\0\1\1\0\1\1\0\1\0\0\1\1') * 33334
    for b, p in zip(sieve, range(3, 1001, 2)):
        if b:
            pp = (p * p - 3) // 2
            sieve[pp::p] = b'\0' * ((500009 - pp) // p + 1)
    tt = {(i * 2 + 3) ** 2 for i, f in enumerate(sieve) if f}
    tt.update((4, 9, 25))
    for i, x in enumerate(map(int, input().split())):
        if x in tt:
            l[i] = 'YES'
    print('\n'.join(l))


if __name__ == '__main__':
    main()