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 *

n = int(input())
N = 1000001
nums = map(int, input().split(' '))

sieve = [True] * N
prime = {2}

for i in range(2, N, 2):
    sieve[i] = False
    
for i in range(3, N, 2):
    if (not sieve[i]):
        continue

    prime.add(i)
    
    for j in range(i*i, N, i):
        sieve[j] = False
        
def is_t_prime(n):
    f = floor(sqrt(n))
    c = ceil(sqrt(n))
    if (f == c and f in prime):
        return True
    else:
        return False
    
for n in nums:
    if (is_t_prime(n)):
        print("YES")
    else:
        print("NO")

# a T-prime is a square of prime