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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.PrintWriter
import kotlin.math.max

data class Query(val a: Int, val b: Int, val c: Int, val d: Int)

fun main() {
    val pw = PrintWriter(System.out)

    val (n, m, q) = readInputLine().split(" ").map { it.toInt() }

    val query = Array(q) { Query(0, 0, 0, 0) }

    repeat(q) {
        val input = readInputLine().split(" ").map { it.toInt() }
        query[it] = Query(input[0] - 1, input[1] - 1, input[2], input[3])
    }

    val arr = IntArray(n) { 1 }

    fun dfs(index: Int, min: Int): Int {
        if (index == n) {
            var ret = 0
            for (qe in query) {
                if (arr[qe.b] - arr[qe.a] == qe.c) {
                    ret += qe.d
                }
            }
            return ret
        }

        var ret = 0

        for (i in min..m) {
            arr[index] = i
            ret = max(ret, dfs(index + 1, i))
        }

        return ret
    }

    pw.println(dfs(1, 1))

    pw.flush()
}

fun readInputLine(): String {
    return readLine()!!
}

// これが全探索で計算量的に問題ないと見抜けないの、数学的素養がなさすぎてつらい
// 競プロ向いていない つらい