A12854. Rectangle Painting 2

There is a square grid of size $n \times n$ . Some cells are colored in black, all others are colored in white. In one operation you can select some rectangle and color all its cells in white. It costs $\min(h, w)$ to color a rectangle of size $h \times w$ . You are to make all cells white for minimum total cost.

The square is large, so we give it to you in a compressed way. The set of black cells is the union of $m$ rectangles.

The first line contains two integers $n$ and $m$ ( $1 \le n \le 10^{9}$ , $0 \le m \le 50$ ) — the size of the square grid and the number of black rectangles.

Each of the next $m$ lines contains 4 integers $x_{i1}$ $y_{i1}$ $x_{i2}$ $y_{i2}$ ( $1 \le x_{i1} \le x_{i2} \le n$ , $1 \le y_{i1} \le y_{i2} \le n$ ) — the coordinates of the bottom-left and the top-right corner cells of the $i$ -th black rectangle.

The rectangles may intersect.

Print a single integer — the minimum total cost of painting the whole square in white.

The examples and some of optimal solutions are shown on the pictures below.