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 typing
import math
import collections


def rit(*args) -> typing.Iterator:
    """Read input and yield split cast values.
    """
    func, funcs = int, (int, float, str)
    sep = " "
    for a in args:
        if a in funcs:
            func = a
        elif isinstance(a, str):
            sep = a
    return map(func, input().strip().split(sep))


def pit(itr: typing.Iterable, sep:str=" ") -> None:
    print(sep.join(map(str, itr)))


def main():
    MAX_CHECK = 10 ** 3
    n = int(input())
    if n > 1:
        xs = rit()
    else:
        xs = [int(input())]


    primes = collections.deque([2])
    for n in range(3, MAX_CHECK + 1):
        for p in primes:
            if n % p == 0:
                break
        else:
            primes.append(n)

    def is_prime(n, primes):
        if n < 2:
            return False
        sq = math.sqrt(n)
        for p in primes:
            if p > sq:
                break
            if n % p == 0:
                return False
        return True

    for x in xs:
        sqi = int(math.sqrt(x))
        if sqi ** 2 == x and is_prime(sqi, primes):
            print("YES")
        else:
            print("NO")


main()