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 readarray(f): return map(f, raw_input().split())
def readint(): return int(raw_input())
def printlist(l): print ' '.join(map(str, l))

n = readint()
X = readarray(int)

P = [True]*(10**6+1)
P[0] = False
P[1] = False
for p in range(10**6+1):
  if P[p]:
    for i in range(p+p,10**6+1,p):
      P[i] = False

for x in X:
  y = int(x**0.5)
  if (y-1)*(y-1) == x:
    y -= 1
  elif (y+1)*(y+1) == x:
    y += 1
  if y*y == x and P[y]:
    print 'YES'
  else:
    print 'NO'