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 PYTHON3):

Solution:
def prime(n):
    v = int(n**0.5)+1
    l = [True for i in range(n+1)]
    l[0] = False
    l[1] = False
    for i in range(2,v):
        if l[i]:
            for j in range(i,n+1,i):
                if j>i and l[j]:
                    l[j] = False
    return l

def div3(n):
    v = int(n**0.5)
    if v**2 == n:
        if table[v]:
            return "YES"
        else:
            return "NO"
    else:
        return 'NO'

n = int(input())
# a = [int(i) for i in input().split()]
a = list(map(int,input().split()))
maxv = int(max(a)**0.5)
table = prime(maxv)
a = map(div3,a)
for i in a:
    print(i)