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 gcd,sqrt

t = int(input())

for _ in range(t):
    n = int(input())
    flag = 0
    for i in range(2,int(sqrt(n))+1):
        if flag:
            break
        if n%i==0:
            divided = n//i
            for j in range(2,int(sqrt(n))+1):
                if divided%j==0 and divided//j > 1 and j!=i and j!= divided//j and i!=divided//j:
                    print("YES")
                    print(j,i,divided//j)
                    flag = 1
                    break
    if not flag:
        print("NO")