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

def solve():
    n = int(input())
    a = 0
    b = 0
    for i in range(2, math.ceil(math.sqrt(n))):
        if n % i == 0:
            a = i
            n //= a
            break
    for i in range(2, math.ceil(math.sqrt(n))):
        if n % i == 0 and i != a:
            b = i
            n //= b
            break
    if a == 0 or b == 0 or n == 1:
        print("NO")
    else:
        print("YES")
        print(a, b, n)




t = int(input())
for _ in range(t):
    solve()