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:
N = input()
X = map(int, raw_input().split())

n = 1000001
t = [1] * n
t[0] = 0
p, f = 2, True
while f:
    for i in xrange(2 * p, n, p):
        t[i - 1] = 0
    f = False
    for p in xrange(p + 1, n):
        if t[p - 1]:
            f = True
            break
pp = set()
for i in xrange(n):
    if t[i]:
        pp.add((i + 1) ** 2)

for x in X:
    if x in pp: print 'YES'
    else: print 'NO'