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 math import sqrt ,ceil
def seive(n):
    l=[True]*(n+1)
    for i in range(2,ceil(sqrt(n))+1):
        if(l[i]):
            for j in range(i*i,n+1,i):
                l[j]=False
    s=set()
    for i in range(2,n+1):
        if(l[i]):
            s.add(i)
    return s
def fun(n,a):
    s=seive(10**6)
    l=[]
    for i in a:
        if(sqrt(i)*sqrt(i)==i and sqrt(i) in s):
            l.append('YES')
        else:
            l.append("NO")
    return l
def main():
    n=int(input())
    a=list(map(int,input().split()))
    print(*fun(n,a),sep='\n')
import threading,sys
max_recur_size = 10**4*2 + 1000
max_stack_size = max_recur_size*500
sys.setrecursionlimit(max_recur_size)
threading.stack_size(max_stack_size)
thread = threading.Thread(target=main)
thread.start()