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 
import math
test=int(input())
for i in range(test):
    n=int(input())
    count=0
    j=2
    temp=n
    ans=[]
    r=math.ceil(math.sqrt(n))
    while count<2 and j<r:
       if n%j==0:
            count+=1
            n//=j
            ans.append(j)
       j+=1
    if count==0 or count<2:
        print('NO')
    else:
        s=1
        for i in ans:
           s*=i
        if temp//s not in ans:
            print('YES')
            print(*ans,temp//s)
        else:
            print('NO')
