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:
def process(n,i,sol):
    for j in range(i+1,int(n**(0.5))+1):
        if n%j==0:
            sol.append(j)
            if len(sol)==1:
                process(n//j,j,sol)
                break
            if len(sol)==2:
                if j!=n//j:
                    sol.append(n//j)
                break
    return sol
                
for _ in range(int(input())):
    n=int(input())
    sol=[]
    process(n,1,sol)
    if len(sol)==3:
        print("YES")
        print(*sol)
    else:
        print("NO")