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
import math
n=int(stdin.readline().rstrip())
l=list(map(int,stdin.readline().split()))
k=[math.sqrt(x) for x in l]
for i in k:
    if i==1:
        print("NO")
    elif math.ceil(i)-i==0.0:
        flag=0
        x=int(math.ceil(math.sqrt(int(i))))
        for j in range(2,x+1):
            if int(i)%j==0 and j!=int(i):
                flag=1
        if flag==1:
            print("NO")
        elif int(i)==2:
            print("YES")
        else:
            print("YES")
    else:
        print("NO")