Many Requirements

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.

Examples

Input

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

Output

110

Input

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

Output

357500

Input

10 10 1 1 10 9 1

Output

1

inputFormat

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

outputFormat

Output

Print the maximum possible score of A.

Examples

Input

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

Output

110

Input

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

Output

357500

Input

10 10 1 1 10 9 1

Output

1

样例

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

110