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 read():
    n = int(input())
    return n


def first_factor(n, from_factor):
    for i in range(from_factor, int(n ** 0.5) + 1):
        if n % i == 0:
            return i
    return None


def solve(n):
    result = [0] * 3
    from_factor = 2
    for i in range(2):
        d = first_factor(n, from_factor)
        if d is not None:
            result[i] = d
            from_factor = d + 1
            n = n // d
        else:
            return None

    if n == result[1]:
        return None
    else:
        result[2] = n

    return result


for t in range(int(input())):
    result = solve(read())
    if result:
        print("YES")
        print(*result)
    else:
        print("NO")