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
t=int(input())
for _ in range(t):
    n=int(input())
    n_root=int(math.sqrt(n))
    ans=[]
    count=0
    for i in range(2,n_root+1):
        if n%i==0:
            ans.append(i)
            count+=1
            n//=i
        if count==2 and n>ans[-1]:
            count+=1
            ans.append(n)
            break
    if count==3:
        print("YES")
        print(*ans)
    else:
        print("NO")