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:
from sys import stdin
from functools import reduce
def solve():
    for _ in range(int(stdin.readline())):
        n=int(stdin.readline())
        #a=list(set(reduce(list.__add__,([i,n//i]for i in range(1,int(n**(.5))+1) if n%i==0))))
        flag,a1,a2,a3,tmp=0,0,0,0,0
        for i in range(2,int(n**.5)+1):
            if flag==1:
                break
            if n%i==0:
                tmp=n//i
                a1=i
                for j in range(2,int((tmp)**.5)+1):
                    if tmp%j==0:
                        a2=j
                        a3=tmp//j
                        if a1!=a2 and a2!=a3 and a3!=a1:
                            flag=1
                            break
        if flag==1:
            print('YES')
            print(a1,a2,a3,sep=' ')
        else:
            print('NO')
        
solve()