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())
a = input().split()
primes = [2]
for k in range(3,1000):
    for i in primes:
        flag = True
        if k%i == 0:
            flag = False
            break
    if flag:
        primes.append(k)
for i in range(n):
    b = int(math.sqrt(int(a[i])))
    if not(b*b == int(a[i])):
        print('NO')
    else:
        done = False
        for k in primes:
            if b > k and b%k == 0:
                print('NO')
                done = True
                break
        if not done:
            c = int(math.sqrt(b))
            flag = False
            for j in range(2,c+1):
                if b%j == 0:
                    flag = True
                    break
            if flag or b == 1:
                print('NO')
            else:
                print('YES')