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-----
3 4 3
1 3 3 100
1 2 2 10
2 3 2 10

-----Sample Output-----
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.

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