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
import math
from collections import defaultdict,Counter

# input=sys.stdin.readline
# def print(x):
#     sys.stdout.write(str(x)+"\n")

# sys.stdout=open("CP1/output.txt",'w')
# sys.stdin=open("CP1/input.txt",'r')

# m=pow(10,9)+7
t=int(input())
for i in range(t):
    n=int(input())
    a=b=c=-1
    d=-1
    for j in range(2,int(math.sqrt(n))+1):
        if n%j==0:
            a=j
            if n//j!=j:
                d=n//j
                break
    if a==-1 or d==-1:
        print("NO")
    else:
        for j in range(2,int(math.sqrt(d))+1):
            if d%j==0 and j!=a:
                b=j
                if d//j!=j:
                    c=d//j
                    break
        if b==-1 or c==-1:
            print("NO")
        else:
            print("YES")
            print(a,b,c)