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:
import math
t=int(input())
while t>0:
    n=int(input())
    flag=-1
    for i in range(2,int(math.sqrt(n))+1):
        if n%i==0:
            for j in range(2,int(math.sqrt(n//i))+1):
                if (n//i)%j==0 and j!=i and (n//j)//i !=j and (n//j)//i !=i and (n//j)//i !=1:
                    flag=1
                    print('YES')
                    print(i,j,(n//i)//j)
                    break
        if flag==1:
            break
    if flag==-1:
        print('NO')
    t-=1