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:
limit = 1000000
def pf():
    prime_flag = [True] * limit
    prime_flag[0] = prime_flag[1] = False
    for i in range(2,limit):
        if prime_flag[i] == True:
            for j in range(i*i, limit, i):
                prime_flag[j] = False
    return prime_flag

n = int(input())
m = list(map(int, input().split()))
pf=pf()
for i in range(n):
    if m[i] == 4:
        print("YES")
        continue
    if m[i] < 4 or m[i] % 2 == 0:
        print("NO")
        continue
    p=m[i]**0.5
    if p==int(p):
        if pf[int(p)]:
            print("YES")
        else:
            print("NO")
    else:
        print("NO")