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:
from sys import stdin
import math
n=int(stdin.readline())
a=stdin.readline().strip().split()
fl =[0]*(10**6+5)
def sq(m):
 n = int(math.sqrt(m))
 return n
def ch():
 hi = 10**6+1
 m = 2
 while m<hi:
  if fl[m]==0:
   cur = 2*m
   while cur<=hi:
    fl[cur] = 1
    cur+=m
  m+=1

ch()
fl[1] = 1
for i in a:
 x = int(i)
 y = sq(x)
 #print " sqr is ",y
 if y*y==x and fl[y]==0:
  print "YES"
 else:
  print "NO"