AtCoder Regular Contest 063 F : Snuke’s Coloring 2 利用性质 单调栈 线段树

F - すぬけ君の塗り絵 2 / Snuke's Coloring 2

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Time limit : 4sec / Memory limit : 256MB

Score : 1600 points

Problem Statement

There is a rectangle in the xy-plane, with its lower left corner at (0,0) and its upper right corner at (W,H). Each of its sides is parallel to the x-axis or y-axis. Initially, the whole region within the rectangle is painted white.

Snuke plotted N points into the rectangle. The coordinate of the i-th (1≦i≦N) point was (xi,yi).

Then, for each 1≦i≦N, he will paint one of the following four regions black:

• the region satisfying x<xi within the rectangle
• the region satisfying x>xi within the rectangle
• the region satisfying y<yi within the rectangle
• the region satisfying y>yi within the rectangle

Find the longest possible perimeter of the white region of a rectangular shape within the rectangle after he finishes painting.

Constraints

• 1≦W,H≦108
• 1≦N≦3×105
• 0≦xi≦W (1≦i≦N)
• 0≦yi≦H (1≦i≦N)
• W, H (21:32, added), xi and yi are integers.
• If i≠j, then xi≠xj and yi≠yj.

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Input

The input is given from Standard Input in the following format:

W H N
x1 y1
x2 y2
:
xN yN

Output

Print the longest possible perimeter of the white region of a rectangular shape within the rectangle after Snuke finishes painting.

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Sample Input 1

Copy

10 10 4
1 6
4 1
6 9
9 4

Sample Output 1

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32

In this case, the maximum perimeter of 32 can be obtained by painting the rectangle as follows:

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Sample Input 2

Copy

5 4 5
0 0
1 1
2 2
4 3
5 4

Sample Output 2

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12

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Sample Input 3

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100 100 8
19 33
8 10
52 18
94 2
81 36
88 95
67 83
20 71

Sample Output 3

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270

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Sample Input 4

Copy

100000000 100000000 1
3 4

Sample Output 4

Copy

399999994

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