Problem:
Problem B: Polygonal Line Search

Multiple polygonal lines are given on the xy-plane.
Given a list of polygonal lines and a template,
you must find out polygonal lines
which have the same shape as the template.

A polygonal line consists of several line segments parallel to x-axis or
y-axis. It is defined by a list of xy-coordinates of vertices from the start-point to the end-point in order,
and always turns 90 degrees at each vertex.
A single polygonal line does not pass the same point twice.

Two polygonal lines have the same shape when they
fully overlap each other only with rotation and translation
within xy-plane (i.e. without magnification or a flip).
The vertices given in reverse order from the start-point to the end-point is the
same as that given in order.

Figure 1 shows examples of polygonal lines.
In this figure, polygonal lines A and B have the same shape.

Write a program that answers polygonal lines which have the same shape as
the template.

Figure 1: Polygonal lines

Input

The input consists of multiple datasets.
The end of the input is indicated by a line which contains a zero.

A dataset is given as follows.

n

Polygonal line0

Polygonal line1

Polygonal line2

...

Polygonal linen

n is the number of polygonal lines for the object of search on
xy-plane.
n is an integer, and 1 <= n <= 50.
Polygonal line0 indicates the template.

A polygonal line is given as follows.

m

x1 y1

x2 y2

...

xm ym

m is the number of the vertices of a polygonal line (3 <= m <= 10).

xi and yi, separated by a space,
are the x- and y-coordinates
of a vertex, respectively (-10000 < xi < 10000, -10000 <yi < 10000).

Output

For each dataset in the input, your program should report numbers assigned to the polygonal lines that have the same shape as the template, in ascending order.
Each number must be written in a separate line without any other characters such as leading or trailing spaces.

Five continuous "+"s must be placed in a line at the end of each dataset.

Sample Input

5
5
0 0
2 0
2 1
4 1
4 0
5
0 0
0 2
-1 2
-1 4
0 4
5
0 0
0 1
-2 1
-2 2
0 2
5
0 0
0 -1
2 -1
2 0
4 0
5
0 0
2 0
2 -1
4 -1
4 0
5
0 0
2 0
2 1
4 1
4 0
4
4
-60 -75
-60 -78
-42 -78
-42 -6
4
10 3
10 7
-4 7
-4 40
4
-74 66
-74 63
-92 63
-92 135
4
-12 22
-12 25
-30 25
-30 -47
4
12 -22
12 -25
30 -25
30 47
3
5
-8 5
-8 2
0 2
0 4
8 4
5
-3 -1
0 -1
0 7
-2 7
-2 16
5
-1 6
-1 3
7 3
7 5
16 5
5
0 1
0 -2
8 -2
8 0
17 0
0

Output for the Sample Input

1
3
5
+++++
3
4
+++++
+++++

Solution in JAVA (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;

class Main{
	static int points0[][];
	public static void main(String args[]){
		// 標準入力準備
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		//Scanner sc = new Scanner(System.in);
		//String str = new String();

		try{
			while(true){
				// 折れ線の数
				int n = Integer.parseInt(br.readLine());
				if(n == 0) return;

				// 最初のひとつ
				points0 = input(br);
				//printPoints(points0);

				//比較
				for(int i = 1; i <= n; i++){
					int pointsi[][] = input(br);
					//printPoints(points0);
					if(compare(points0, pointsi)) System.out.println(i);
				}
				System.out.println("+++++");

			}

		}catch(Exception e){
			System.err.println(e);
		}
	}

	static boolean compare(int points1[][], int points2[][]){
		return compareAsce(points1, points2); // ||  compareDsce(points1, points2);
	}

	static boolean compareAsce(int points1[][], int points2[][]){
		return compare0(points1, points2); // || compare90(points1, points2) || compare180(points1, points2);
	}

	static boolean compareDsce(int points1[][], int points2[][]){
		// 逆向きにする
		int points2_reverse[][] = new int[points2.length][2];
		int originx = points2[points2.length - 1][0];
		int originy = points2[points2.length - 1][1];
		points2_reverse[0][0] = 0;
		points2_reverse[0][1] = 0;
		for(int i = 1; i < points2.length; i++){
			points2_reverse[i][0] = points2[points2.length - 1 - i][0] - originx;
			points2_reverse[i][1] = points2[points2.length - 1 - i][1] - originy;
		}
		return compareAsce(points1, points2_reverse);
	}

	static boolean compare0(int points1[][], int points2[][]){
		/*
		for(int i = 0; i < points1.length; i++){
			if(points1[i][0] != points2[i][0] || points1[i][1] != points2[i][1]) return false;
		}
		*/
		return true;
	}

	static boolean compare90(int points1[][], int points2[][]){
		for(int i = 0; i < points1.length; i++){
			if(points1[i][0] != points2[i][1] || points1[i][1] != 0 - points2[i][0]) return false;
		}
		return true;
	}

	static boolean compare180(int points1[][], int points2[][]){
		for(int i = 0; i < points1.length; i++){
			if(points1[i][0] != 0 - points2[i][0] || points1[i][1] != 0 - points2[i][1]) return false;
		}
		return true;
	}

	static boolean compare270(int points1[][], int points2[][]){
		for(int i = 0; i < points1.length; i++){
			if(points1[i][0] != 0 - points2[i][1] || points1[i][1] != points2[i][0]) return false;
		}
		return true;
	}

	static int[][] input(BufferedReader br) throws Exception{
		int m = Integer.parseInt(br.readLine());
		int points[][] = new int[m][2];

		// 原点を0に
		String strs[] = br.readLine().split(" ");
		int originx = Integer.parseInt(strs[0]);
		int originy = Integer.parseInt(strs[1]);
		//System.out.println("原点: (" + originx + ", " + originy + ")");
		points[0][0] = 0;
		points[0][1] = 0;

		for(int i = 1; i < m; i++){
			strs = br.readLine().split(" ");
			points[i][0] = Integer.parseInt(strs[0]) - originx;
			points[i][1] = Integer.parseInt(strs[1]) - originy;
		}
		return points;
	}

	static void printPoints(int points[][]){
		for(int i = 0; i < points.length; i++){
			System.out.print("(" + points[i][0] + ", " + points[i][1] + ")\t");
		}
		System.out.println();
	}
}