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 collections import *
from bisect import *
from math import *
from heapq import *
from fractions import *
import sys
input=sys.stdin.readline
t=1
def r(a):
    return ((a*(a-1))//2)
while(t):
    t-=1
    n=int(input())
    a=list(map(int,input().split()))
    for i in a:
        c=pow(i,0.5)
        if(c*c!=i or ceil(c)!=floor(c)):
            print("NO")
            continue
        c=int(c)
        if((c%2==0 and c!=2) or c==1):
            print("NO")
            continue
        s=0
        for j in range(3,int(pow(c,0.5))+1,2):
            if(c%j==0):
                s=1
                break
        if(not(s)):
            print("YES")
        else:
            print("NO")