D-Cutting with Lines Ⅰ_2022年浙大城市学院新生程序设计竞赛（同步赛）

时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

There is a matrix in the 2D plane, whose vertices labelled as $(0,0)$ , $(n, 0)$ , $(0, m)$ and $(n, m)$ .

$333lfy$ has $q$ segments. The length of the $i$ -th segment is $a_i$ . He wants to place these segments in this 2D plane.

There are following four ways to place the $i$ -th segment:

$1$ $x$ --- The coordinates of the endpoints of the $i$ -th segment are $(x,m)$ and $(x,m - a_i)$ .
$2$ $x$ --- The coordinates of the endpoints of the $i$ -th segment are $(x,\ 0)$ and $(x,\ a_i)$ .
$3$ $x$ --- The coordinates of the endpoints of the $i$ -th segment are $(0,\ x)$ and $(a_i,\ x)$ .
$4$ $x$ --- The coordinates of the endpoints of the $i$ -th segment are $(n,\ x)$ and $(n - a_i,\ x)$ 。

After placing all segments, the matrix is divided into several parts by these segments. Now please calculate the area of the largest part.

输入描述:

The first line of the input contains three integers   --- The position of the matrix and the number of the segments.The size of the matrix and the number of the segments.

The next The next  lines each line contains three integers, and the -th line belong to one of the following four types:
           --- The length of the -th segment is  and the coordinates of the endpoints are  and .
           --- The length of the -th segment is  and the coordinates of the endpoints are  and .
           --- The length of the -th segment is  and the coordinates of the endpoints are  and .
           --- The length of the -th segment is  and the coordinates of the endpoints are  and .

输出描述:

Print one integer — the number satisfying the conditions above.

示例1

输入

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输出

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说明

The example is shown in the figure：