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 itertools import combinations
from math import sqrt
for _ in range(int(input())):
    l=[]
    n=int(input())
    for i in range(2,int(sqrt(n))+1):
        if n%i==0:
            if n//i!=i:
                l.append(i)
                l.append(n//i)
            else:
                l.append(i)
    if len(l)<3:
        print("NO")
    else:
        k=combinations(l,3)
        for i in k:
            if i[0]*i[1]*i[2]==n:
                print("YES")
                print(i[0],i[1],i[2])
                break
        else:
            print("NO")