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

def sieve(n):
    isPrime = [True] * n
    isPrime[0] = False
    isPrime[1] = False
    i = 2
    while i * i <= n:
        if isPrime[i]:
            j = i+i
            while j < n:
                isPrime[j] = False
                j += i
        i += 1
    return isPrime

def isTNumber(num, sieve):
    if num < 4: return False
    squareroot = math.sqrt(num)
    if squareroot.is_integer(): 
        return sieve[int(squareroot)]
    return False

n = int(input())
nums = [int(val) for val in input().split()]
sieve = sieve(1000001)
for num in nums:
    print("YES" if isTNumber(num, sieve) else "NO")