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 is_prime(n: int) -> bool:
    if n == 2 or n == 3:
        return True
    elif n % 2 == 0 or n < 2:
        return False
    elif n < 9:
        return True
    elif n % 3 == 0:
        return False
    for i in range(5, int(n**0.5)+1, 6):
        if n % i == 0:
            return False
        if n % (i + 2) == 0:
            return False
    return True


input()
x = [(int(i) ** 0.5) for i in input().split()]
for i in x:
    print(['NO', ['NO', 'YES'][is_prime(int(i))]][i % 1 == 0])