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:
for _ in range(int(input())):
    n = int(input())

    ok = False
    c = 2
    while not ok and c*c*c <= n:
        if n % c != 0:
            c += 1
            continue

        # a * b = n / c
        # a > b > c
        b = c+1
        while not ok and b*b <= (n // c):
            if (n // c) % b != 0:
                b += 1
                continue

            a = n // (c * b)
            if a > b:
                print('YES')
                print(a, b, c)
                ok = True

            b += 1

        c += 1

    if not ok:
        print('NO')