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:
oo = 10**6
p = [True] * (oo+1)

def primes():
    global p
    p[0] = p[1] = False
    for i in range(int(oo**0.5)+1):
        if (p[i]):
            j = i*i
            while(True):
                if j > oo: break
                p[j] = False
                j += i

primes()

def isSquare(k):
    ck = int(k**0.5)
    if ck*ck == k:
        return True
    return False

n = input()
sn = input()
for v in sn.split():
    u = int(v)
    if isSquare(u) and p[int(u**0.5)]:
        print('YES')
    else: print('NO')