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 go():
    m = 10 ** 6
    m_sq = m ** 2
    n = int(input())
    a = [int(i) for i in input().split(' ')]
    sieve = [True] * (m)
    for i in range(2, m):
        if sieve[i] == True:
            for j in range(i ** 2, m, i):
                sieve[j] = False
    s = set(i for i in range(2, m) if sieve[i])
    o = ''
    from math import sqrt
    for i in a:
        sq = sqrt(i)
        if int(sq) == sq:
            if sq in s:
                o += 'YES\n'
            else:
                o += 'NO\n'
        else:
            o += 'NO\n'
    return o

print(go())