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:
for i in range(int(input())):
    n=int(input())
    i=2
    arr=[]
    while n>0 and i<=(int(n**0.5)):
        if n%i==0:
            n/=i
            arr.append(i)
        i+=1
        if len(arr)==2:
            break
    if len(arr)==2:
        if n not in arr:
            print('YES')
            print(arr[0],arr[1],int(n))
        else:
            print('NO')
    else:
        print('NO')