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())
    r=[]
    q=2
    i=0
    while i<2 and q<=math.sqrt(n):
        if n%q==0:
            r.append(q)
            i+=1
            n=n//q
        q+=1
    if n!=1:
        r+=[n]
    if len(r)<3 or r[1]==r[2] or r[0]==r[2] or r[0]==r[1]:
        print('NO')
    else:
        print('YES')
        print(*r)