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 sys import stdin,stdout,maxsize;# mod = int(1e9 + 7);#import re  # can use multiple splits
# tup = lambda: map(int, stdin.readline().split())
I = lambda: int(stdin.readline())
lint = lambda: [int(x) for x in stdin.readline().split()]
# S = lambda: stdin.readline().replace('\n', '').strip()
# #def grid(r, c): return [lint() for i in range(r)]
# #def debug(*args, c=6): print('\033[3{}m'.format(c), *args, '\033[0m', file=stderr)
stpr = lambda x  : stdout.write(f'{x}' + '\n')
# star = lambda x : print(' '.join(map(str , x)))
# from _collections import defaultdict
# from math import ceil
N = int(1e6) + 1
a = [1]*N
d= {}
for i in range(2 ,N):
    if a[i]:
        for j in range(i*i , N , i):
            a[j] = 0
        d[i*i] = True
I()
for i in lint():
    try:
        if d[i] ==True:
            stpr("YES")
    except KeyError:stpr("NO")