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 math
T=int(input())
for i in range((T)):
    x=input()
    x=int(x)
    d=0
    a,b,c=-1,-1,-1
    p=x
    for j in range(2,int(math.sqrt(x))+1):
        if x%j==0:
            a=j
            x=x//j
            break
    if a!=-1:
        for j in range(a+1,int(math.sqrt(x))+1):
            if x%j==0:
                b=j
                x=x//j
                break
    if p%x==0:
        c=x
    if a==-1 or b==-1 or c==-1 or b==c or a==c:
        print("NO")
    else:
        print("YES")
        print(a,b,c,sep=" ")