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:
import math


p = [True for i in range(1000003)]


def init():
    p[0] = p[1] = False
    for i in range(2, 1000003):
        if p[i]:
            for j in range(i, 1000003 // i + 1):
                p[i * j] = False


def is_square(x):
    return int(math.sqrt(x)) * int(math.sqrt(x)) == x


def is_prime(x):
    return p[x]


def t_primes(n, a):
    res = []
    for x in a:
        if is_square(x) and is_prime(int(math.sqrt(x))):
            res.append("YES")
        else:
            res.append("NO")
    return res


if __name__ == "__main__":
    init()
    n = int(input())
    a = list(map(int, input().split()))
    result = t_primes(n, a)
    print(*result, sep='\n')