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 bisect import bisect_left


def main():
    input()
    tt = [4]
    limit = 1000004
    lim2 = limit // 2 - 1
    sieve = [True] * lim2
    for i in range(lim2 // 3 + 1):
        if sieve[i]:
            p, pp = 2 * i + 3, (i + 3) * i * 2 + 3
            sieve[pp::p] = [False for _ in range(pp, lim2, p)]
    for i, f in enumerate(sieve):
        if f:
            i += i + 3
            tt.append(i * i)
    for x in map(int, input().split()):
        print(('NO', 'YES')[tt[bisect_left(tt, x)] == x])


if __name__ == '__main__':
    main()