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 collections import defaultdict

def solve(n):
    table = set()
    i = 2
    while i*i <= n:
        if n % i == 0:
            table.add(i)
            n /= i
            break
        i += 1

    i = 2
    while i*i <= n:
        if n % i == 0 and i not in table:
            table.add(i)
            n /= i
            break
        i += 1

    if len(table) < 2 or n == 1 or n in table:
        print("NO")
    else:
        print("YES")
        table.add(int(n))

        print(" ".join([str(t) for t in table]))

T = int(input())
for t in range(T):
    n = int(input())

    solve(n)