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:
# cook your dish here
import math
t=int(input())
for _ in range(t):
    count=0
    a=[]
    n=int(input())
    for i in range(2,int(math.sqrt(n))):
        
        if (n%i==0 and count<2):
            n=int(n/i)
            a.append(i)
            count+=1
    if n not in a and n!=1:
        a.append(n)
        count+=1
    if count == 3:
        print('YES')
        for i in a:
            print(i,end=" ")
        print("")
    else:
        
        print("NO")