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 ni():
    return int(raw_input())

def nis():
    return map(int, raw_input().split())

def get_tprimes(n):
    tprimes = []

    n = int(math.ceil(math.sqrt(n)))

    # find all primes, up to ncrt
    is_prime = [False, False]
    is_prime.extend([True for _ in xrange(2, n + 1)])

    for i in xrange(2, n + 1):
        if not is_prime[i]:
            continue
        for j in xrange(i + i, n + 1, i):
            is_prime[j] = False

        tprimes.append(i**2)

    return set(tprimes)

n = ni()
a = nis()
max_a = max(a)

tprimes = get_tprimes(max_a)

ans = [None] * n
i = 0
for x in a:
    ans[i] = 'YES' if x in tprimes else 'NO'
    i += 1

print '\n'.join(ans)