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:
from math import *

N = 1000009

primes = []
bs = [1]*(N+10)

def sieve():
    _sieve_size = N + 2
    bs[0] = bs[1] = 0
    for i in range(2,_sieve_size):
        if(bs[i]):
            for j in range(i*i,_sieve_size,i):
                bs[j] = 0
            primes.append(i)

sieve()
n = int(raw_input())
ins = raw_input()
ins = ins.split()
ins = map(int,ins)
for x in ins:
    if(sqrt(x).is_integer()):
        if(bs[int(sqrt(x))] == 1):
            print "YES"
        else:
            print "NO"
    else:
        print "NO"