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:
from math import sqrt 
primes=[True for i in range(1000001)]
primes[1]=False
def SieveOfEratosthenes(n):  
    p = 2
    while (p * p <= n): 
          
        # If prime[p] is not changed, then it is a prime 
        if (primes[p] == True): 
              
            # Update all multiples of p 
            for i in range(p * p, n+1, p): 
                primes[i] = False
        p += 1

def isThreeDisctFactors(n): 
    sq = int(sqrt(n)) 

    if (1 * sq * sq != n): 
        return False

    if (primes[sq]==True): 
        return True
    else: 
        return False

if __name__ == '__main__': 
    t=int(input())
    nums=list(map(int,input().split()))
    SieveOfEratosthenes(1000000)
    for i in nums:
        if(isThreeDisctFactors(i)):
            print("YES")
        else:
            print("NO")