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


def is_prime(foo):
    if foo % 3 == 0 or foo % 2 == 0 or foo < 1:
        if foo == 3 or foo == 2:
            return True
        else:
            return False
    bar = int(sqrt(foo))
    for i in range(5, bar + 1, 2):
        if foo % i == 0:
            return False
    return True


def is_t(bar):
    if bar == 1:
        return False
    foo = bar ** 0.5
    if foo != int(foo):
        return False
    return is_prime(int(foo))


n = int(input())
x = list(map(int, input().split()))
for xi in x:
    if is_t(xi):
        print('YES')
    else:
        print('NO')