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:
'''input
1
999993399999
'''

import sys
from math import *
from collections import defaultdict
from string import ascii_lowercase as lcs
from string import ascii_uppercase as ucs
from fractions import Fraction, gcd
from decimal import Decimal, getcontext
from itertools import product, permutations, combinations, count
#getcontext().prec = 500
sys.setrecursionlimit(30000)

mod = 10**9 + 7

raw_input = lambda: sys.stdin.readline().rstrip()
die = lambda : exit(0)
flush= lambda : sys.stdout.flush()

r_s = lambda: raw_input()                   #read str
r_ss = lambda: raw_input().split()          #read stringss
r_i = lambda: int(raw_input())              #read int
r_is = lambda: map(int, raw_input().split())#read ints
r_f = lambda: float(raw_input())            #read float
r_fs = lambda: map(Decimal, raw_input().split()) #read floats

# For effieciently taking lots of queries with each query in a separate line
# having integer values separated by space. A 2d list is made with each row
# corresponding to line. Each row is a list with all the values.
r_qs = lambda: map(lambda s:map(int, s.split(' ')), sys.stdin.readlines())

'''-------------------------------------------------------------------'''


n = int(raw_input())
x = r_is()
s = set()
z = 10**6+3
primes = [1]*z
for k in range(2, z):
    if primes[k]==1:
        s.add(k**2)
        primes[k**2::k] = [0]*(z/k - k + 1)

print "\n".join(["NO", "YES"][k in s] for k in x)