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:
if __name__ == "__main__":
    primes = [True] * 1000000
    primes[1] = primes[0] = False
    for j in range(2, 1000000):
        if primes[j] == True:
            for k in range(j*j, 1000000, j):
                primes[k] = False
    tests = int(input())
    num_array = [int(i) for i in input().split()]
    for j in num_array:
        if j == 4:
            print("YES")
            continue
        if j < 4 or j % 2 == 0:
            print("NO")
            continue
        sqr = j**0.5
        if int(sqr) == sqr:
            if primes[int(sqr)] == True:
                print("YES")
                continue
        print("NO")
        continue