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 as m
n1=int(1e6)
prime=[True for i in range(n1+1)]
prime[0]=False
prime[1]=False
p=2
while p*p<=n1:
    if prime[p]==True:
        for i in range(p*p,n1+1,p):
            prime[i]=False
    p+=1
prime=[i*i for i in range(n1+1) if prime[i]==True] 
def search(a,t):
    l,r=0,len(a)-1
    while l<=r:
        mid=l+(r-l)//2
        if a[mid]==t:
            return 1
        elif a[mid]<t:
            l=mid+1
        else:
            r=mid-1
    else:
        return -1
        
n=int(input())
a=list(map(int,input().split()))
for i in a:
    if search(prime,i)==1:
        print("YES")
    else:
        print("NO")