Problem Statement

A fantastic IS is an integer sequence of length N whose every element is between 1 and M (inclusive) that satisfies the following condition.

• For every integer i such that $1 \le i \le K,$ one of the following holds.
• A_{P_i} < X_i and A_{Q_i} < Y_i;
• A_{P_i} = X_i and A_{Q_i} = Y_i;
• A_{P_i} > X_i and A_{Q_i} > Y_i.

Determine whether a fantastic IS exists. If it does, find the minimum possible sum of the elements in a fantastic IS.

Input

Input is given from Standard Input in the following format:
N M K
P_1 X_1 Q_1 Y_1
P_2 X_2 Q_2 Y_2
$\vdots$
P_K X_K Q_K Y_K

Output

If a fantastic IS exists, print the minimum possible sum of the elements in a fantastic IS; otherwise, print -1.

Constraints

• $1 \le N,M,K \le 2 \times 10^5$
• $1 \le P_i,Q_i \le N$
• $1 \le X_i,Y_i \le M$
• $P_i \neq Q_i$
• All values in input are integers.

Sample Input 1

3 4 3
3 1 1 2
1 1 2 2
3 4 1 4

Sample Output 1

6

A=(2,3,1) fully satisfies the condition and thus is a fantastic IS, whose sum of the elements is 6.
There is no fantastic IS whose sum of the elements is less than 6, so the answer is 6.

Sample Input 2

2 2 2
1 1 2 2
2 1 1 2

Sample Output 2

-1

There is no fantastic IS, so -1 should be printed.

Sample Input 3

5 10 10
4 1 2 7
5 1 3 2
2 9 4 4
5 4 2 9
2 9 1 9
4 8 3 10
5 7 1 5
3 5 1 2
3 8 2 10
2 9 4 8

Sample Output 3

12

见题面 Input 部分

见题面 Output 部分