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


N = int(1e12)

tprimes = {}
sieve = []

#largest prime where prime*prime would be <= 1e12
def setup():
    n = int(1e6)
    sieve = [True for _ in xrange(n+1)]
    sieve[0] = False
    sieve[1] = False
    for i in xrange(2, n):
        if sieve[i]:
            tprimes[i*i] = 0
            for j in xrange(i+i, n, i):
                sieve[j] = False



def main():
    n = int(raw_input())
    arr = map(int, raw_input().split())
    setup()
    for i in arr:
        print "YES" if i in tprimes else "NO"
main()