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
x=int(input())
for _ in range(x):
    n=int(input())
    c=0
    lol=set()
    f=0
    for i in range(2,int(math.sqrt(n))+1):
        
        if n%i==0:
            k=i
            while n%k==0:
                
                n//=k
                lol.add(k)
                c+=1
                k*=i
                #print(n,k,i)
                if len(lol)==2:
                    f=1
                    break
            if f:
                break
    if n>=2:
        lol.add(n)
    if f and len(lol)==3 :
        print("YES")
        print(*lol)
    else:
        print("NO")