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
from collections import defaultdict as dc
import math
from bisect import bisect, bisect_left,bisect_right
input=sys.stdin.readline
for _ in range(int(input())):
    n=int(input())
    i=2
    f=0
    #p=math.sqrt(n)
    while(i<=math.sqrt(n)):
        if n%i==0:
            f=1
            break
        i+=1
    if f==0:
        #print("c1")
        print("NO")
    else:
        f=0
        n=n//i
        j=2
        while(j<=math.sqrt(n)):
            if j not in [1,i] and n%j==0:
                f=1
                break
            j+=1
        if f==0:
            #print("c2")
            print("NO")
        else:
            n=n//j
            if i!=j and n!=i and n!=j:
                print("YES")
                print(i,j,n)
            else:
                print("NO")