Director K loves fortune-telling and often performs various kinds. Today, he decided to use cards to predict the performance of this year's Japanese IOI team.

The method of fortune-telling is as follows:

• First, arrange all cards in a rectangular grid with $M$ rows and $N$ columns, all facing face-up.
• For each $i = 1, \dots, K$, perform the operation: "Flip all cards located from the $A_i$-th to the $B_i$-th row from the top, and from the $C_i$-th to the $D_i$-th column from the left." That is, if we denote the card at the $a$-th row from the top and $b$-th column from the left as $(a, b)$, for each $i$, flip all cards $(a, b)$ that satisfy $A_i \le a \le B_i$ and $C_i \le b \le D_i$.
• After the operations are finished, the result of the fortune-telling is determined by the number of cards that are face-up.

Director K realized that the number of times he would have to flip the cards is too large, so he decided not to use the cards to perform the fortune-telling, but instead to calculate only the number of cards that are face-up after the operations are finished.

Task

Given the number of rows $M$, the number of columns $N$, the number of operations $K$, and the instructions for the $K$ operations, write a program to calculate the number of cards that are face-up after the operations.

Constraints

• $1 \le M \le 1\,000\,000\,000 (= 10^9)$
• $1 \le N \le 1\,000\,000\,000 (= 10^9)$
• $1 \le K \le 100\,000 (= 10^5)$

Input

Read the following from standard input:

• The first line contains three space-separated integers $M, N, K$, representing that the cards are arranged in $M$ rows and $N$ columns, and that there are $K$ operations to be performed.
• The $(1 + i)$-th line ($1 \le i \le K$) contains four integers $A_i, B_i, C_i, D_i$ ($1 \le A_i \le B_i \le M, 1 \le C_i \le D_i \le N$), representing that the $i$-th operation flips all cards from the $A_i$-th to the $B_i$-th row and from the $C_i$-th to the $D_i$-th column.

Output

Output the number of cards that are face-up after $K$ operations in a single line to standard output.

Subtasks

For 30% of the test cases, $K \le 3\,000$.

Examples

Input 1

6 5 3
2 4 1 4
4 6 3 5
1 2 3 5

Output 1

11

Note

In this example, the $K = 3$ operations are performed as follows. Representing face-up cards as $\square$ and face-down cards as $\blacksquare$:

Initial state: $\square\square\square\square\square$ $\square\square\square\square\square$ $\square\square\square\square\square$ $\square\square\square\square\square$ $\square\square\square\square\square$ $\square\square\square\square\square$

$\downarrow$

$\square\square\square\square\square$ $\blacksquare\blacksquare\blacksquare\blacksquare\square$ $\blacksquare\blacksquare\blacksquare\blacksquare\square$ $\blacksquare\blacksquare\blacksquare\blacksquare\square$ $\square\square\square\square\square$ $\square\square\square\square\square$

$\downarrow$

$\square\square\square\square\square$ $\blacksquare\blacksquare\blacksquare\blacksquare\square$ $\blacksquare\blacksquare\blacksquare\blacksquare\square$ $\blacksquare\blacksquare\square\square\blacksquare$ $\square\square\blacksquare\blacksquare\blacksquare$ $\square\square\blacksquare\blacksquare\blacksquare$

$\downarrow$

$\square\square\blacksquare\blacksquare\blacksquare$ $\blacksquare\blacksquare\square\square\blacksquare$ $\blacksquare\blacksquare\blacksquare\blacksquare\square$ $\blacksquare\blacksquare\square\square\blacksquare$ $\square\square\blacksquare\blacksquare\blacksquare$ $\square\square\blacksquare\blacksquare\blacksquare$

Final state: The number of face-up cards in the final state is 11.