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())
for i in range(t):
    s=int(input())
    s1=0
    d=0
    f=0
    for j in range(2,int(math.sqrt(s))+1):
        if s%j==0:
            s1=j
            d=s/j
            for k in range(2,int(math.sqrt(d))+1):
                if d%k==0:
                    s2=k
                    s3=d/k
                    if s2!=s3 and s3!=s1 and s2!=s1:
                        print("YES")
                        print(int(s1),int(s2),int(s3))
                        f=1
                        break
            if f==1:
                break
            for k in range(2,int(math.sqrt(s1))+1):
                if s1%k==0:
                    s2=k
                    s3=s1/k
                    if s2!=s3 and s3!=d and s2!=d:
                        print("YES")
                        print(int(s1),int(s2),int(s3))
                        f=1
                        break
            if f==1:
                break
    if f==0:
      print("NO")