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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

"use strict";
var __importStar = (this && this.__importStar) || function (mod) {
    if (mod && mod.__esModule) return mod;
    var result = {};
    if (mod != null) for (var k in mod) if (Object.hasOwnProperty.call(mod, k)) result[k] = mod[k];
    result["default"] = mod;
    return result;
};
Object.defineProperty(exports, "__esModule", { value: true });
var fs = __importStar(require("fs"));
{
    var isDebug = false;
    var main = function (args) {
        var _a = parser_1(args), a = _a.a, b = _a.b, n = _a.n;
        var result = maxFloor_1(a, b, n);
        console.log(result);
    };
    var parser_1 = function (inputStr) {
        var _a = inputStr.split(' '), aStr = _a[0], bStr = _a[1], nStr = _a[2];
        return {
            a: Number(aStr),
            b: Number(bStr),
            n: Number(nStr),
        };
    };
    var maxFloor_1 = function (a, b, n) {
        if (b - 1 < n) {
            return Math.floor((a * (b - 1)) / b) - (a * Math.floor((b - 1) / b));
        }
        else {
            return Math.floor((a * n) / b) - (a * Math.floor(n / b));
        }
    };
    if (isDebug) {
        var Q1 = '5 7 4';
        main(Q1);
    }
    else {
        main(fs.readFileSync('/dev/stdin', 'utf8'));
    }
}