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 atexit
import io
import sys
from bisect import *
from collections import *
from fractions import gcd
from itertools import *
from math import *
import os

inf = float('inf')
inf_neg = float('-inf')
range_6 = int(1e7+1)
range_7 = int(1e6+1)
range_8 = int(1e8+1)


_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER
@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())

def rwh_primes_jason(n):
    """ Input n>=6, Returns a list of primes, 2 <= p < n """
    zero = bytearray([False])
    size = n//3 + (n % 6 == 2)
    sieve = bytearray([True]) * size
    sieve[0] = False
    for i in range(int(n**0.5)//3+1):
      if sieve[i]:
        k=3*i+1|1
        start = (k*k+4*k-2*k*(i&1))//3
        sieve[(k*k)//3::2*k]=zero*((size - (k*k)//3 - 1) // (2 * k) + 1)
        sieve[  start ::2*k]=zero*((size -   start  - 1) // (2 * k) + 1)
    ans = [2,3]
    poss = chain.from_iterable(zip_longest(*[range(i, n, 6) for i in (1,5)]))
    ans.extend(compress(poss, sieve))
    return ans

def main():
    # code here
    # testing on set (hashable) && segmented 
    
    primes = rwh_primes_jason(range_7)
    

    primes_sq = set()
    for i in primes:
        primes_sq.add(i*i)



    n = int(input())
    arr = list(map(int, input().split()))
    for j in arr:
        if j in primes_sq:
            print("{}".format('YES'))
        else:
            print("{}".format('NO'))
        


if __name__ == '__main__':
    
    main()