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 PYTHON):

Solution:
import math


def eratosthenes(n):
    """http://stackoverflow.com/a/3941967/239076"""
    # Initialize list of primes
    _primes = [True] * n

    # Set 0 and 1 to non-prime
    _primes[0] = _primes[1] = False

    for i, is_prime in enumerate(_primes):
        if is_prime:
            yield i

            # Mark factors as non-prime
            for j in range(i * i, n, i):
                _primes[j] = False


PRIMES = set(eratosthenes(10**6))

_ = raw_input()

for n in (int(x) for x in raw_input().split()):
    s = math.sqrt(n)
    if s * s == n:
        print 'YES' if s in PRIMES else 'NO'
    else:
        print 'NO'