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:
n = int(input())
l = [int(x) for x in input().split()]
def primes(n):
  f = []
  for i in range(n+1):
    if i > 2 and i%2 == 0:
      f.append(0)
    else:
      f.append(1)
 
  i = 3
  while i*i <= n:
    if f[i] == 1:
      j = i*i
      while j <= n:
        f[j] = 0
        j += i+i
    i += 2
 
  return f

p = primes(10 ** 6)

for i in range(n):
    if l[i] == 1:
        print('NO')
    else:
        k = l[i] ** 0.5
        if k % 1 == 0:
            if p[int(k)] == 1:
                print('YES')
            else:
                print('NO')
        else:
            print('NO')