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)

fun main(arr:Array<String>) {
    val (n,m,q) = readLine()!!.split(" ").map { it.toInt() }
    val req = (1..q).map { readLine()!!.split(" ").map { it.toInt() }.let { Require(it) } }
    val solve = Solve(m, req)
    var ans = 0
    for(i in (1..m)) {
        val arr = (1..n).map { 1 }.toTypedArray()
        arr[0] = i
        ans = Math.max(ans, solve.getAns(1, arr))
    }
    println(ans)
}

class Require(num:List<Int>) {
    val index1 = num[0] - 1
    val index2 = num[1] - 1
    val diff = num[2]
    val score = num[3]
}
class Solve(val maxNum:Int, val requireList:List<Require>) {
    fun getAns(index:Int, arr:Array<Int>):Int {
        if(index >= arr.size) {
            return getScore(arr)
        }

        var ans = 0
        for(i in (arr[index-1]..maxNum)) {
            arr[index] = i
            ans = Math.max(ans, getAns(index+1, arr))
        }
        return ans
    }

    fun getScore(arr:Array<Int>):Int {
        var score = 0
        for(req in requireList) {
            if(arr[req.index2] - arr[req.index1] == req.diff) {
                score+=req.score
            }
        }
        return score
    }
}