4672: Recover Polygon (medium)
内存限制：256 MB
时间限制：2 S
题面：传统
评测方式：文本比较
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题目描述
B2. Recover Polygon (medium)
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Now that Heidi has made sure her Zombie Contamination level checker works, it's time to strike! This time, the zombie lair is a strictly convex polygon on the lattice. Each vertex of the polygon occupies a point on the lattice. For each cell of the lattice, Heidi knows the level of Zombie Contamination — the number of corners of the cell that are inside or on the border of the lair.
Given this information, Heidi wants to know the exact shape of the lair to rain destruction on the zombies. Help her!
Given this information, Heidi wants to know the exact shape of the lair to rain destruction on the zombies. Help her!
Input
The input contains multiple test cases.The first line of each test case contains one integer N, the size of the lattice grid (5≤N≤500). The next N lines each contain N characters, describing the level of Zombie Contamination of each cell in the lattice. Every character of every line is a digit between 0 and 4.
Cells are given in the same order as they are shown in the picture above: rows go in the decreasing value of y coordinate, and in one row cells go in the order of increasing x coordinate. This means that the first row corresponds to cells with coordinates (1,N),...,(N,N) and the last row corresponds to cells with coordinates (1,1),...,(N,1).
The last line of the file contains a zero. This line should not be treated as a test case. The sum of the N values for all tests in one file will not exceed 5000.
Output
For each test case, give the following output:The first line of the output should contain one integer V, the number of vertices of the polygon that is the secret lair. The next V lines each should contain two integers, denoting the vertices of the polygon in the clockwise order, starting from the lexicographically smallest vertex.
Examples
Input
8 00000000 00000110 00012210 01234200 02444200 01223200 00001100 00000000 5 00000 01210 02420 01210 00000 7 0000000 0122100 0134200 0013200 0002200 0001100 0000000 0
Output
4 2 3 2 4 6 6 5 2 4 2 2 2 3 3 3 3 2 3 2 5 4 5 4 2
Note
It is guaranteed that the solution always exists and is unique. It is guaranteed that in the correct solution the coordinates of the polygon vertices are between 2 and N-2. A vertex (x1,y1) is lexicographically smaller than vertex (x2,y2) if x1<x2 or 
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