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:
import math

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

    n = int(input())

    a = b = c = -1;

    ok = 0;

    for j in range(2, int(math.sqrt(n))+1):
        if n % j == 0:
            if a == -1:
                a = j;
                n /= a
            elif b == -1:
                b = j;
                n /= b;
                if (n >= 2 and n != a and n != b):
                    c = n;
                    ok = 1;
                else:
                    break
    if ok:
        print("YES")
        print(a, b, int(c))
    else:
        print("NO")