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:
from math import ceil, sqrt
 
t = int(input())
for _ in range(t):
    n = int(input())
    if n < 24:
        print('NO')
    else:
        try:
            for i in range(4, ceil(sqrt(n)) + 1):
                if n % i == 0:
                    a = n // i
                    b = i
                    for j in range(2, ceil(sqrt(a))):
                        if a % j == 0 and j != b and a // j != b and a // j > 1:
                            print('YES')
                            print(b, j, a // j)
                            raise SystemExit
                    for j in range(2, ceil(sqrt(b))):
                        if b % j == 0 and j != a and b // j != a and b // j > 1:
                            print('YES')
                            print(a, j, b // j)
                            raise SystemExit
        except SystemExit:
            continue
        else:
            print('NO')