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 math
 
n = int(input())
nums = list(map(int, input().split(' ')))

max_num = max(nums)
m = int(math.sqrt(max_num)) + 1
prime = [True for i in range(m)] 
p = 2
while (p * p <= m): 
    if (prime[p] == True): 
        for i in range(p * 2, m, p): 
            prime[i] = False
    p += 1
prime[0]= False
prime[1]= False
 
for num in nums:
    sq_rt = math.sqrt(num)
    if sq_rt.is_integer():
        if prime[int(sq_rt)] == True:
            print("YES")
        else:
            print("NO")
    else:
        print("NO")