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:
def sieve():
  l = [True]*(10**6+2)
  l[0],l[1],l[2] = False,False,True
  for i in range(2,len(l)):
    #print i
    if l[i]:
      #print i
      for j in range(2*i,len(l),i):
        if l[j]:l[j] = False
  return l
m = sieve()
#print m
n = int(raw_input())
l = map(int,raw_input().split())
for  i in l:
  if i==1:print "NO";continue
  if i**0.5 == int(i**0.5):
    if m[int(i**0.5)]:print "YES"
    else: print "NO"
  else: print "NO"