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 i in range(int(input())):
    n=int(input())
    l=[]
    count=0
    for i in range(2,int(math.sqrt(n))+1):
        if n%i==0:
            l.append(i)
            n=n//i
            break
    for i in range(2,int(math.sqrt(n))+1):
        if n%i==0 and len(l)==1 and l[0]!=i:
            l.append(i)
            n=n//i
            count=1
            break
    flag=0
    if count==1:
        if n!=l[0] and n!=l[1]:
            l.append(n)
    else:
        flag=1
    
    if len(l)==3 and flag==0:
        print("YES")
        print(*l)
    else:
        print("NO")