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):
    t-=1
    n=int(input())
    ans=-1
    if n<24:
        print("NO")
        continue
    else:
        root=int(math.sqrt(n))
        factors=set()
        for i in range(2,root+1):
            if n%i==0:
                factors.add(i)
                factors.add(n//i)
       # print (factors)
        for i in factors:
            for j in factors:
                s=n//(i*j)
                if i!=j and s in factors:
                    if i!=s and j!=s:
                        ans = []
                        ans.append(i)
                        ans.append(j)
                        ans.append(s)
                        ans.sort()
                        break
            if ans!=-1:
                break
    if ans==-1:
        print("NO")
        #print(ans)
    else:
        print("YES")
        print(*ans)