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
for _ in range(int(input())):
    n=int(input())
    flag=0
    for i in range(2,math.ceil(math.sqrt(n))+1):
        l=[]
        if n%i==0:
            l.append(i)
            a=n//i
            for j in range(2,math.ceil(math.sqrt(a))+1):
                if a%j==0 and j!=l[-1]:
                    l.append(j)
                    break
            if len(l)<2:
                continue
            b=n//(l[0]*l[1])
            if b!=l[0] and b!=l[1] and b!=1:
                l.append(b)
                print("YES")
                print(*l)
                flag=1
                break
            else:
                continue
    if flag==0:
        print("NO")