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 sys
from math import sqrt, ceil
from sys import setrecursionlimit

setrecursionlimit( 10 **5 )
# sys.stdin = open("input.txt", "r")
# sys.stdout = open("output.txt", "w")

readline = sys.stdin.readline

# SOLUTION
# observer t_primes are squares of prime number.
# t_primes <= 10^12
# max number = sqrt(10^12) = 10^6
# use sieve of eratosthenes to find prime numbers till (10^6)

# similar to sieve of eratosthenes
def util():
    a = set()

    n = 10 ** 6
    prime = [True] * (n+1)
    p=2
    while p <= n:
        if prime[p]:
            # modified it according to qn.
            # append the prime square
            a.add(p*p)
            for i in range(p*2, n+1, p):
                prime[i] = False
        p+=1
    
    prime[0] = prime[1] = False
    return a

def process():
    _ = int(readline())
    arr = map(int, readline().rstrip().split())
    # O(10^6)
    prime = util()

    for i in arr:
        print("YES") if i in prime else print("NO")

#for _ in range(int(readline())):
process()