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 Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int M = sc.nextInt();
		int Q = sc.nextInt();
		int[] a = new int[Q];
		int[] b = new int[Q];
		int[] c = new int[Q];
		int[] d = new int[Q];
		for(int i = 0; i < Q; i++) {
			a[i] = sc.nextInt();
			b[i] = sc.nextInt();
			c[i] = sc.nextInt();
			d[i] = sc.nextInt();
		}
		int ans = 0;
		int[] A = new int[N];
		A[0] = 1;
		if(N == 2) {
			for(int i = 1; i <= M; i++) {
				A[1] = i;
				int temp = 0;
				for(int r = 0; r < Q; r++) {
					if(A[b[r]-1]-A[a[r]-1] == c[r])
						temp += d[r];
				}
				ans = Math.max(ans, temp);
			}
		}
		else if(N == 3) {
			for(int i = 1; i <= M; i++) {
				A[1] = i;
				for(int j = i; j <= M; j++) {
					A[2] = j;
					int temp = 0;
					for(int r = 0; r < Q; r++) {
						if(A[b[r]-1]-A[a[r]-1] == c[r])
							temp += d[r];
					}
					ans = Math.max(ans, temp);
				}
			}
		}
		else if(N == 4) {
			for(int i = 1; i <= M; i++) {
				A[1] = i;
				for(int j = i; j <= M; j++) {
					A[2] = j;
					for(int k = j; k <= M; k++) {
						A[3] = k;
						int temp = 0;
						for(int r = 0; r < Q; r++) {
							if(A[b[r]-1]-A[a[r]-1] == c[r])
								temp += d[r];
						}
						ans = Math.max(ans, temp);
					}
				}
			}
		}
		else if(N == 5) {
			for(int i = 1; i <= M; i++) {
				A[1] = i;
				for(int j = i; j <= M; j++) {
					A[2] = j;
					for(int k = j; k <= M; k++) {
						A[3] = k;
						for(int l = k; l <= M; l++) {
							A[4] = l;
							int temp = 0;
							for(int r = 0; r < Q; r++) {
								if(A[b[r]-1]-A[a[r]-1] == c[r])
									temp += d[r];
							}
							ans = Math.max(ans, temp);
						}
					}
				}
			}
		}
		else if(N == 6) {
			for(int i = 1; i <= M; i++) {
				A[1] = i;
				for(int j = i; j <= M; j++) {
					A[2] = j;
					for(int k = j; k <= M; k++) {
						A[3] = k;
						for(int l = k; l <= M; l++) {
							A[4] = l;
							for(int m = l; m <= M; m++) {
								A[5] = m;
								int temp = 0;
								for(int r = 0; r < Q; r++) {
									if(A[b[r]-1]-A[a[r]-1] == c[r])
										temp += d[r];
								}
								ans = Math.max(ans, temp);
							}
						}
					}
				}
			}
		}
		else if(N == 7) {
			for(int i = 1; i <= M; i++) {
				A[1] = i;
				for(int j = i; j <= M; j++) {
					A[2] = j;
					for(int k = j; k <= M; k++) {
						A[3] = k;
						for(int l = k; l <= M; l++) {
							A[4] = l;
							for(int m = l; m <= M; m++) {
								A[5] = m;
								for(int n = m; n <= M; n++) {
									A[6] = n;
									int temp = 0;
									for(int r = 0; r < Q; r++) {
										if(A[b[r]-1]-A[a[r]-1] == c[r])
											temp += d[r];
									}
									ans = Math.max(ans, temp);
								}
							}
						}
					}
				}
			}
		}
		else if(N == 8) {
			for(int i = 1; i <= M; i++) {
				A[1] = i;
				for(int j = i; j <= M; j++) {
					A[2] = j;
					for(int k = j; k <= M; k++) {
						A[3] = k;
						for(int l = k; l <= M; l++) {
							A[4] = l;
							for(int m = l; m <= M; m++) {
								A[5] = m;
								for(int n = m; n <= M; n++) {
									A[6] = n;
									for(int o = n; o <= M; o++) {
										A[7] = o;
										int temp = 0;
										for(int r = 0; r < Q; r++) {
											if(A[b[r]-1]-A[a[r]-1] == c[r])
												temp += d[r];
										}
										ans = Math.max(ans, temp);
									}
								}
							}
						}
					}
				}
			}
		}
		else if(N == 9) {
			for(int i = 1; i <= M; i++) {
				A[1] = i;
				for(int j = i; j <= M; j++) {
					A[2] = j;
					for(int k = j; k <= M; k++) {
						A[3] = k;
						for(int l = k; l <= M; l++) {
							A[4] = l;
							for(int m = l; m <= M; m++) {
								A[5] = m;
								for(int n = m; n <= M; n++) {
									A[6] = n;
									for(int o = n; o <= M; o++) {
										A[7] = o;
										for(int p = o; p <= M; p++) {
											A[8] = p;
											int temp = 0;
											for(int r = 0; r < Q; r++) {
												if(A[b[r]-1]-A[a[r]-1] == c[r])
													temp += d[r];
											}
											ans = Math.max(ans, temp);
										}
									}
								}
							}
						}
					}
				}
			}
		}
		else if(N == 10) {
			for(int i = 1; i <= M; i++) {
				A[1] = i;
				for(int j = i; j <= M; j++) {
					A[2] = j;
					for(int k = j; k <= M; k++) {
						A[3] = k;
						for(int l = k; l <= M; l++) {
							A[4] = l;
							for(int m = l; m <= M; m++) {
								A[5] = m;
								for(int n = m; n <= M; n++) {
									A[6] = n;
									for(int o = n; o <= M; o++) {
										A[7] = o;
										for(int p = o; p <= M; p++) {
											A[8] = p;
											for(int q = p; q <= M; q++) {
												A[9] = q;
												int temp = 0;
												for(int r = 0; r < Q; r++) {
													if(A[b[r]-1]-A[a[r]-1] == c[r])
														temp += d[r];
												}
												ans = Math.max(ans, temp);
											}
										}
									}
								}
							}
						}
					}
				}
			}
		}
		System.out.println(ans);
	}

}