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 PYTHON):

Solution:
import math

def eratosthenes(n):
    P = [True] * (n + 1)
    P[0], P[1] = False, False
    p = 2
    while True:
        for i in range(p * p, n + 1, p):
            P[i] = False
        if p**2 >= n:
            break
        p += 1
    return P

def perfect_square(xi):
    result = int((math.sqrt(xi)))
    if result**2 == xi:
        return True
    return False

def prime_number(n):
    if n == 1:
        return False
    if n % 2 == 0 and n > 2: 
        return False
    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))

primes = eratosthenes(10**6)
n = int(raw_input())
line = map(int, raw_input().split())

for xi in line:
    if (perfect_square(xi) == True) and (primes[int(math.sqrt(xi))] == True):
        print "YES"
    else:
        print "NO"