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:
t = int(input())
for _ in range(t) :
    n = int(input())
    i = 2
    k = 1
    x = 1
    y = 1 
    z = 1
    flag = 0
    while i*i<=n :
        if n%i==0 :
            if k==1 :
                x = i
                n = n//i
                k = 0
            elif n//i != i and x!=i and x!= n//i:
                y = i 
                z = n//i
                break
            else :
                flag = 1 
                break
        i += 1 
    if flag == 0 and x>1 and y>1 and z>1:
        print("YES")
        print(x,y,z)
    else :
        print("NO")