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 sieve(n: int) -> list:
    ary = [True]*(n+1)
    ary[0] = ary[1] = False

    for i in range(4, n+1, 2):
        ary[i] = False

    m = int(n**0.5) + 1
    for i in range(3, m, 2):
        if ary[i]:
            for j in range(i*i, n+1, i):
                ary[j] = False
    return ary

n = int(input())
ary = list(map(int, input().strip().split()))
prime_bool = sieve(int(max(ary)**0.5))
for i in ary:
    if i**0.5 - int(i**0.5) == 0:
        if prime_bool[int(i**0.5)]: print("YES")
        else: print("NO")
    else:
        print("NO")