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:
primes = []

def generate_primes(LIMIT):
    global primes
    primes = [True]*LIMIT
    primes[0],primes[1] = False, False
    for i in range(2,LIMIT):
        if primes[i]:
            for j in range(i*i,LIMIT,i):
                primes[j] = False

def is_perfect_square(number):
    sqr = number**0.5
    return sqr == int(sqr)

def is_t_prime(numbers):
    for number in numbers:
        if number % 2 == 0:
            if number != 4:
                print("NO")
            else:
                print("YES")
        else:
            if is_perfect_square(number) and primes[int(number**0.5)]:
                print("YES")
            else:
                print("NO")

def main():
    generate_primes(1000000)
    n = int(input())
    numbers = list(map(int,input().split()))
    is_t_prime(numbers)

main()