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 get_primes(n):
    P = [1] * (n+1)
    P[0] = P[1] = 0
    for i in xrange(2,int(n**0.5)+1):
        st = i*2
        end = n+1
        for j in xrange(st,end,i):
            P[j] = 0
    return P
def solve():
    import math
    n = input()
    A = map(int, raw_input().split())
    P = get_primes(int(max(A)**0.5))
    for e in A:
        sqrt_e = int(math.ceil(e**0.5))
        if sqrt_e*sqrt_e == e and P[sqrt_e] == 1:
            print "YES"
        else:
            print "NO"

solve()