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())
from math import sqrt
for i in range(t):
    number=int(input())
    l=[]
    for i in range(2,int(sqrt(number))+1):
        if number%i==0:
            for j in range(2,int(sqrt(number//i))+1):
                if (number//i)%j==0 and j!=i and (number//i)//j not in[i,j]:
                    l.append(i)
                    l.append(j)
                    l.append((number//i)//j)
                    break
    if len(l)%3==0 and len(l)!=0:
        print('YES')
        print(*l[0:3])
    else:
        print('NO')