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 math import sqrt 

x=int(input())
y=list(map(int,input().strip().split(' ')))

limit=10**6
arr=[1]*(limit//2)

pos=lambda i:(i//2)-1

def prime_generate():
  for i in range(3,int(sqrt(limit)),2):
    if arr[ pos(i) ]:
      for ii in range(i**2,limit,i*2):
        arr[ pos(ii) ] = 0

def prime_check(n):
	if n==1: return False
	if n==2: return True
	if n%2==0: return False

	return arr[pos(n)]

perfect_root_check = lambda i: int(sqrt(i))**2==i

prime_generate()
	

for i in y:
  if i==4:
    print("YES")
  elif perfect_root_check(i) and prime_check( int(sqrt(i)) ):
    print("YES")
  else:
    print("NO")