Catarina loves all cats that live in her neighborhood. Her lifelong dream is to design a large cat-seeing circuit, so that every day she can go out and greet the cats while doing some exercise. Catarina's neighborhood can be represented as the 2D plane, with the North-South direction aligned with the -axis. A cat-seeing circuit that visits cats consists of exactly steps. Catarina chooses a starting position and faces one of the four cardinal directions. For each step the following occurs:
Catarina chooses a value and walks units from straight ahead in her current direction, stopping at the location of a cat that she has not greeted during any previous step.
Catarina greets the cat, taking some time to appreciate its beauty.
Without turning around, Catarina walks another units straight ahead in her current direction, stopping at a position .
Catarina turns either clockwise or counterclockwise, facing again one of the four cardinal directions.
After completing all steps, Catarina must be back to her starting position , facing her initial direction. Notice that the length of the cat-seeing circuit is . When , the cat-seeing circuit has length .
Catarina knows the location of the cats that live in her neighborhood. Surprisingly, no two cats have the same -coordinate or the same -coordinate. Your task is to determine the maximum length that a cat-seeing circuit can have.
输入格式
The first line contains an integer () indicating the number of cats.
Each of the next lines describes a cat with two integers and (), representing that the cat has coordinates .
No two cats have the same -coordinate or -coordinate (they differ in both of them).
输出格式
Output a single line with an integer indicating the maximum length that a cat-seeing circuit can have.
样例
样例输入 1
5
1 2
2 1
0 0
-1 -2
-2 -1
样例输出 1
0
样例输入 2
6
4 0
0 4
2 -1
-1 2
-4 3
3 -4
样例输出 2
32
样例输入 3
7
2 1
0 -1
5 5
3 0
4 4
6 2
1 -2
样例输出 3
24
数据范围与提示
Explanation of Sample 1:
In this case there is a circuit of length that visits all the cats, but it is not a cat-seeing circuit because the cat at coordinates is greeted twice.
Explanation of Sample 2:
The picture below shows the location of the cats with small circles, together with a maximum-length cat-seeing circuit that visits all of them. The length of the circuit is .
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Explanation of Sample 3:
It is possible to visit of the cats with a cat-seeing circuit of length .
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