Problem:
Score : 300 points

Problem Statement

Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).

Consider a sequence A satisfying the following conditions:

A is a sequence of N positive integers.

1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M.

Let us define a score of this sequence as follows:

The score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0.)

Find the maximum possible score of A.

Constraints

All values in input are integers.

2 ≤ N ≤ 10

1 \leq M \leq 10

1 \leq Q \leq 50

1 \leq a_i < b_i \leq N ( i = 1, 2, ..., Q )

0 \leq c_i \leq M - 1 ( i = 1, 2, ..., Q )

(a_i, b_i, c_i) \neq (a_j, b_j, c_j) (where i \neq j)

1 \leq d_i \leq 10^5 ( i = 1, 2, ..., Q )

Input

Input is given from Standard Input in the following format:

N M Q
a_1 b_1 c_1 d_1
:
a_Q b_Q c_Q d_Q

Output

Print the maximum possible score of A.

Sample Input 1

3 4 3
1 3 3 100
1 2 2 10
2 3 2 10

Sample Output 1

110

When A = \{1, 3, 4\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.

Sample Input 2

4 6 10
2 4 1 86568
1 4 0 90629
2 3 0 90310
3 4 1 29211
3 4 3 78537
3 4 2 8580
1 2 1 96263
1 4 2 2156
1 2 0 94325
1 4 3 94328

Sample Output 2

357500

Sample Input 3

10 10 1
1 10 9 1

Sample Output 3

1

Solution in Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

N, M, Q = gets.split.map(&:to_i)
@a = $<.read.split.map(&:to_i).each_slice(4).to_a.sort

@max = 0
key = Array.new(N+1, -1)
key[0] = 1

def solve(aaa, value, i)
    arr = Marshal.load(Marshal.dump(aaa))
    #puts "v:#{value} i:#{i} #{aaa}"
    @max = value if @max < value
    return if Q <= i
    
    if arr[@a[i][0]] == -1
        1.upto(@a[i][0]).each do |j|
            arr[j] = arr[j-1] 
        end
    end
    
    #採用しない
    solve(arr, value, i+1)
    
    #採用
    #puts "sai + #{arr} + #{@a[i]}"
    
    if arr[@a[i][1]] == -1
        arr[@a[i][1]] = arr[@a[i][0]] + @a[i][2]
        #puts "#{@a[i][0]} #{@a[i][1]} h:#{arr[@a[i][1]]} #{arr[@a[i][0]]} + #{@a[i][2]}"
    end
    
    return if M < arr[@a[i][1]] 
    
    if(arr[@a[i][1]] == arr[@a[i][0]] + @a[i][2])
        solve(arr, value + @a[i][3], i+1)
    end
end

solve(key, 0, 0)

puts @max