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:
v = int(input())
for i in range(v):
    b = list(map(int,input().split()))[:v]
    c = 0
    a = []
    for j in b:
        for h in range(2,int(j**(0.5))+1):
            if j%h==0:
                c+=1
                j = j//h
                a.append(h)
                if len(a)==2:
                    break
        if len(a)==2 and j not in a:
            print("YES")
            print(*a,j)
            
        else:
            print("NO")