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 = 10**6

def rwh_primes(n):
  sieve = [True] * n
  for i in range(3,int(n**0.5)+1,2):
    if sieve[i]:
      sieve[i*i::2*i]=[False]*((n-i*i-1)//(2*i)+1)
  return [2] + [i for i in range(3,n,2) if sieve[i]]

pq = set([v*v for v in rwh_primes(N)])
n = int(input())
for v in map(int, input().split()):
  if v in pq:
    print("YES")
  else:
    print("NO")