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
import math
def precompute_prime_square():
    n = 10**6
    prime = [True]*(n+1)
    p = 2
    sett = set()
    while p*p<=n:
        if prime[p]:
            for i in range(p*p,n+1,p):
                prime[i] = False
        p+=1
    for i in range(2,n):
        if prime[i]:
            sett.add(i**2)
    return sett
def solution(sett):
    n = int(sys.stdin.readline())
    arr = list(map(int,sys.stdin.readline().split()))
    for i in arr:
        if i in sett:
            print("YES")
        else:
            print("NO")


if __name__=="__main__":
    sett = precompute_prime_square()
    solution(sett)