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:
from collections import Counter, defaultdict
from sys import stdin, stdout
raw_input = stdin.readline

for t in xrange(input()):
    n=input()
    l=[]
    f=0
    for i in xrange(2,min(n+1,10001)):
        if n%i==0:
            l.append(i)
            n/=i
        if len(l)==2 and n not in l and n>1:
            f=1
            break
        elif len(l)==2:
            break
    if f:
        stdout.write('YES\n')
        for j in l:
            stdout.write(str(j)+' ')
        stdout.write(str(n)+'\n')
    else:
        stdout.write('NO\n')