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: Wrong Answer)

#!/usr/bin/env ruby
n, m, q = gets.chomp.split.map(&:to_i)


a = []
b = []
c = []
d = []

1.upto(q) do |i|
  input = gets.chomp.split.map(&:to_i)
  a << input[0]
  b << input[1]
  c << input[2]
  d << input[3]
end

ans = 0

1.upto(10) do |i_1|
  a_1 = i_1
  1.upto(10) do |i_2|
    a_2 = i_2
    next if a_2 < a_1
    1.upto(10) do |i_3|
      a_3 = i_3
      next if a_3 < a_2
      1.upto(10) do |i_4|
        a_4 = i_4
        next if a_4 < a_3
        1.upto(10) do |i_5|
          a_5 = i_5
          next if a_5 < a_4
          1.upto(10) do |i_6|
            a_6 = i_6
            next if a_6 < a_5
            1.upto(10) do |i_7|
              a_7 = i_7
              next if a_7 < a_6
              1.upto(10) do |i_8|
                a_8 = i_8
                next if a_8 < a_7
                1.upto(10) do |i_9|
                  a_9 = i_9
                  next if a_9 < a_8
                  1.upto(10) do |i_10|
                    a_10 = i_10
                    next if a_10 < a_9

                    arr = [nil, a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8, a_9, a_10]
                    score = 0
                    a.each_with_index do |a_i, i|
                      score += d[i] if arr[b[i]] - arr[a_i] == c[i]
                    end
                    ans = score if score > ans
                  end
                end
              end
            end
          end
        end
      end
    end
  end
end

puts ans