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 PYTHON):

Solution:
import sys
for _ in range(input()):
    n=input()
    flag=0
    for i in range(2,int(n**(0.5))+1):
        if n%i==0:
            a=i
            s=n/i
            b=0
            c=0
            for j in range(2,int(s**(0.5)+1)):
                if s%j==0 and a!=j:
                    b=j
                    c=s/j
                if a!=b and b!=c and a!=c and a>=2 and b>=2 and c>=2:
                    print "YES"
                    arr= [a,b,c]
                    arr.sort()
                    for i in arr:
                        print i,
                    print
                    flag=1
                    break
        if flag:
            break
    else:
        print "NO"