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:
import math

marked = [ 0 for x in xrange(0,1000000)]
marked[2] = 1

for x in xrange(3,1000000,2):
    if marked[x] == 1:
        continue
    if x*x > 1000000:
        continue
    for y in xrange(x*x,1000000,x):
        marked[y] = 1

n = int(raw_input())
p = raw_input().split()
for x in p:
    s = math.floor(math.sqrt(long(x)))
    if long(x) == 1:
        print "NO"
        continue
    if s*s != long(x):
        print "NO"
        continue
    if int(s) == 2:
        print "YES"
        continue
    if int(s) % 2 == 0:
        print "NO"
        continue
    if marked[int(s)] == 0:
        print "YES"
    else:
        print "NO"