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 i in range(0,t):
    n = int(input())
    tmp = n
    lst = []
    j = 2 
    while(j*j<=n) :
        if(tmp%j==0):
            tmp = int(tmp/j)
            lst.append(j)
            if(len(lst)>=2):
                if(tmp>j): lst.append(tmp)
                break
        j = j+1
    
    if(len(lst)==3):
        print("YES")
        print(lst[0]," ",lst[1]," ",lst[2])
    else:
        print("NO")