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 sys
ip = lambda : sys.stdin.readline().rstrip()
for _ in range(int(ip())):
    n=int(ip())
    ans=[]
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            v=n//i
            for j in range(2,int(v**0.5)+1):
                if v%j==0:
                    st=set([i,j,v//j])
                    if len(st)==3:
                        ans=sorted([i,j,v//j])
                        break
            if ans!=[]:
                break
    if ans!=[]:
        print("YES")
        print(*ans)
    else:
        print("NO")