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:
t = int(input())
while t > 0:
    res = []
    n = int(input())
    root = int(n**.5)
    while root > 1:
        if n % root == 0:
            rem = n/root
            rem_root = int(rem**.5)
            if rem == rem_root**2:
                root -= 1
                continue
            else:
                while rem_root > 1:
                    if rem % rem_root == 0:

                        if rem_root == root or (rem/rem_root) == root:
                            rem_root -= 1
                            continue
                        else:
                            res = [root, int(rem_root), int(rem/rem_root)]
                            print(f'YES\n{root} {int(rem_root)} {int(rem/rem_root)}')
                            break
                    rem_root -= 1
        if len(res) == 3:
            break
        root -= 1
    t -= 1
    if len(res) != 3:
        print('NO')