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:
# Same logic with sieve giving TLE
import math
sq = int(math.sqrt(1000000))
li = [0] * 1000002
li[0] = 1
li[1] = 1
for x in xrange(2, sq):
    if li[x] == 0:
        j = x * x
        while j <= 1000000:
            li[j] = 1
            j += x

n = int(raw_input())
nn=raw_input().split()
for x in nn:
     m=int(math.sqrt(int(x)))
     if m*m==int(x):
        if li[m]==0:
           print 'YES'
        else:
           print 'NO'
     else:
        print 'NO'