Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in PYTHON3):

Solution:
def else1(N):
    for a in range(2, int(N ** (1. / 3)) + 1):
        for b in range(a + 1, int((N // a) ** 0.5) + 1):
            c = N // a // b
            if a * b * c == N and c != a and c != b:
                print('YES')
                print(a, b, c)
                return
    else:
        print('NO')

def main():
    t = int(input())
    for i in range(t):
        N = int(input())
        L = []
        if N ** (1./3) < 0.9:
            print('NO')
        else:
            else1(N)
main()