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())
data=input().split()
def isprime(x):
    if x==1:
        return 0
    elif x in (2,3,5,7,11,13,17,19):
        return 1
    elif x%2==0 or x%3==0 or x%5==0 or x%7==0 or x%11==0 or x%13==0 or x%17==0 or x%19==0:
        return 0
    else:
        for i in range(2,int(math.sqrt(x))+1):
            if x%i==0:
                return 0
        return 1

for i in range(n):
    num=int(data[i])
    c="NO"
    if num==1 or num==2 or num==3:
        print(c)
    else:
        q=math.sqrt(num)
        if q%1==0.0:
            if isprime(int(q)):
                print("YES")
            else:
                print("NO")
        else:
            print("NO")