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 PYTHON):

Solution:
import Queue
from collections import Counter
import math
#sys.stdin = open('input.txt', 'r')
#sys.stdout = open('output.txt','w')

N = int(raw_input().strip())
A = map(int, raw_input().strip().split(' '))

MAX = 10**6 + 1
P = [1]*MAX
P[0],P[1] = 0,0
for i in xrange(2,MAX) :
    if i*i >= MAX :
        break
    for j in xrange(i*i,MAX,i) :
        P[j] = 0



for x in A :
    y  = pow(x,0.5)
    y = int(y)
    if x == y*y and P[y] == 1 :
        print 'YES'
    else :
        print 'NO'