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())
s=list(map(int,input().split()))

def factors(n):
    z=int(math.sqrt(n))
    if(z*z!=n):
        return "NO"
    else:
        k=5
        for i in range(z):
            if k*k<=z:
                if z%k==0 or z%(k+2)==0:
                    return "NO"
                k=k+6
            else:
                break
    return "YES"

    
for i in s:
    if i==4 or i==9 or i==25 or i==49:
        print("YES")
    elif i==1:
        print("NO")
    elif i%2==0 and i!=4:
        print("NO")
    elif i%3==0 and i!=9:
        print("NO")
    elif i%5==0 and i!=25:
        print("NO")
    else:
        print(factors(i))