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(n) :
    a = [0, 0, 1] + [1, 0] * (n//2)
    for i in xrange(3, int(n ** .5) + 1, 2) :
        if a[i] :
            for j in xrange(i * i, n, 2 * i) :
                a[j] = 0
    return [p for p in xrange(2, n) if a[p]]

prime = sieve(1000000)
a = {}
for i in prime :
    a[i*i] = 1
n = int(raw_input())
p = map(int, raw_input().split())

for i in p :
    if a.has_key(i) :
        print "YES"
    else :
        print "NO"