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 sys import stdin


def binary_search(data, val):
    highIndex = len(data)-1
    lowIndex = 0
    while highIndex > lowIndex:
        index = (highIndex + lowIndex) // 2
        sub = data[index]
        if data[lowIndex] == val:
            return [lowIndex, lowIndex]
        elif sub == val:
            return [index, index]
        elif data[highIndex] == val:
            return [highIndex, highIndex]
        elif sub > val:
            if highIndex == index:
                return sorted([highIndex, lowIndex])
            highIndex = index
        else:
            if lowIndex == index:
                return sorted([highIndex, lowIndex])
            lowIndex = index
    return sorted([highIndex, lowIndex])


def SieveOfEratosthenes(n):
    all_prime = []

    prime = [True for i in range(n + 1)]
    p = 2
    while p * p <= n:
        if prime[p]:

            for i in range(p * p, n + 1, p):
                prime[i] = False
        p += 1

    for p in range(2, n):
        if prime[p]:
            all_prime.append(p)
    all_prime = [i*i for i in all_prime]
    return all_prime

n = 10**6
r = SieveOfEratosthenes(n)

z = int(input())
l = list(map(int, stdin.readline().rstrip().split(" ")))

for i in l:
    if i >=4:
        a = binary_search(r, i)
        if a[0]==a[1]:
            print("YES")
        else:
            print("NO")
    else:
        print("NO")