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 sys

T = int(sys.stdin.readline())
for _ in range(T):
    n = int(sys.stdin.readline())
    res = set()
    start_i = 2
    for _ in range(2):
        for i in range(start_i, int(n**0.5)+1):
            if not n%i:
                n//=i
                start_i=i+1
                res.add(i)
                break
    res.add(n)
    if len(res)==3:
        print('YES')
        [print(a, end=' ') for a in res]
        print()
    else:
        print('NO')