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 
from math import ceil
def find(n,p,ans):
    for i in range(2,ceil(n**(1/p))+1,1):
        if n%i==0:
            if p==3:
                ans+=find(n//i,2,[i])
                if len(set(ans))==3:
                    return ans
                ans=[]
            elif p==2 and n//i>1:
                new=ans+[(n//i),i]
                if len(set(new))==3:
                    return new
    return ans

for i in range(int(input())):
    n=int(input())
    k=find(n,3,[])
    if len(k)==3:
        print("YES")
        print(*k,sep=" ")
    else:
        print("NO")
