Problem:
Score : 900 points

Problem Statement

AtCoDeer the deer has N square tiles. The tiles are numbered 1 through N, and the number given to each tile is written on one side of the tile. Also, each corner of each tile is painted in one of the 1000 colors, which are represented by the integers 0 between 999. The top-left, top-right, bottom-right and bottom-left corner of the tile with the number i are painted in color C_{i,0}, C_{i,1}, C_{i,2} and C_{i,3}, respectively, when seen in the direction of the number written on the tile (See Figure 1).

Figure 1: The correspondence between the colors of a tile and the input

AtCoDeer is constructing a cube using six of these tiles, under the following conditions:

For each tile, the side with the number must face outward.

For each vertex of the cube, the three corners of the tiles that forms it must all be painted in the same color.

Help him by finding the number of the different cubes that can be constructed under the conditions.
Since each tile has a number written on it, two cubes are considered different if the set of the used tiles are different, or the tiles are used in different directions, even if the formation of the colors are the same. (Each tile can be used in one of the four directions, obtained by 90° rotations.) Two cubes are considered the same only if rotating one in the three dimensional space can obtain an exact copy of the other, including the directions of the tiles.

Figure 2: The four directions of a tile

Constraints

6≦N≦400

0≦C_{i,j}≦999 (1≦i≦N , 0≦j≦3)

Input

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

N
C_{1,0} C_{1,1} C_{1,2} C_{1,3}
C_{2,0} C_{2,1} C_{2,2} C_{2,3}
:
C_{N,0} C_{N,1} C_{N,2} C_{N,3}

Output

Print the number of the different cubes that can be constructed under the conditions.

Sample Input 1

6
0 1 2 3
0 4 6 1
1 6 7 2
2 7 5 3
6 4 5 7
4 0 3 5

Sample Output 1

1

The cube below can be constructed.

Sample Input 2

8
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 1

Sample Output 2

144

Sample Input 3

6
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0

Sample Output 3

122880

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map.Entry;

public class Main {
	InputStream is;

	int __t__ = 1;
	int __f__ = 0;
	int __FILE_DEBUG_FLAG__ = __f__;
	String __DEBUG_FILE_NAME__ = "src/C2";

	FastScanner in;
	PrintWriter out;

	long XXX = 10000;
	long toKey(int[] c) {
		long key = Long.MAX_VALUE;
		for (int i = 0; i < 4; i++) {
			long curKey = 0;
			for (int j = 0; j < 4; j++) curKey = curKey * XXX + c[(i+j)%4];
			if (key > curKey) key = curKey;
		}
		return key;
	}
	
	HashMap<Long, Long> hash = new HashMap<>();
	void add(long key) {
		if (hash.containsKey(key))
			hash.put(key, hash.get(key) + 1);
		else
			hash.put(key, 1L);
	}
	
	int comb(long key) {
		long[] vals = new long[4];
		for (int i = 0; i < 4; i++) {
			vals[i] = key % XXX;
			key /= XXX;
		}
		if (vals[0] == vals[1] && vals[1] == vals[2] && vals[2] == vals[3])
			return 4;
		else if (vals[0] == vals[2] && vals[1] == vals[3])
			return 2;
		else
			return 1;
	}
	
	long get(long key) {
		if (!hash.containsKey(key)) return 0;
		return hash.get(key);
	}
	
	public void solve() {
		int N = in.nextInt();
		
		int[][] C = new int[N][4];
		for (int i = 0; i < N; i++) {
			for (int j = 0; j < 4; j++) {
				C[i][j] = in.nextInt();
			}
			long key = toKey(C[i]);
			add(key);
			System.out.println(Arrays.toString(C[i]) + " " + key);
		}
		
		long res = 0;
		for (int c1 = 0; c1 < N; c1++) {
			for (int c2 = c1 + 1; c2 < N; c2++) {
				int x1 = C[c1][0], x2 = C[c1][1], x3 = C[c1][2], x4 = C[c1][3];
				int y1 = C[c2][1], y2 = C[c2][0], y3 = C[c2][3], y4 = C[c2][2];
				long xkey = toKey(new int[]{x1, x2, x3, x4});
				long ykey = toKey(new int[]{y1, y2, y3, y4});
				for (int rotate = 0; rotate < 4; rotate++) {
					long upKey     = toKey(new int[]{y1, y2, x2, x1});
					long bottomKey = toKey(new int[]{y3, y4, x4, x3});
					long rightKey  = toKey(new int[]{x3, x2, y2, y3});
					long leftKey   = toKey(new int[]{x1, x4, y4, y1}); 
					
					long ucnt = get(upKey) * comb(upKey);
					long bcnt = get(bottomKey) * comb(bottomKey);
					long rcnt = get(rightKey) * comb(rightKey);
					long lcnt = get(leftKey) * comb(leftKey);
					
					long[] keys = {upKey, bottomKey, rightKey, leftKey};
					long[] cnts = {ucnt, bcnt, rcnt, lcnt};
					for (int i = 0; i < 4; i++) {
						if (xkey == keys[i]) cnts[i] -= comb(keys[i]);
						if (ykey == keys[i]) cnts[i] -= comb(keys[i]);
						for (int j = i + 1; j < 4; j++)
							if (keys[i] == keys[j]) cnts[i] -= comb(keys[i]);
					}

					long val = 1;
					for (long c : cnts) val *= c; 
					res += val;
					
					int ytmp = y1;
					y1 = y2;
					y2 = y3;
					y3 = y4;
					y4 = ytmp;
				}
			}
		}
		System.out.println(res/3);
	}
	
	public void run() {
		if (__FILE_DEBUG_FLAG__ == __t__) {
			try {
				is = new FileInputStream(__DEBUG_FILE_NAME__);
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
			System.out.println("FILE_INPUT!");
		} else {
			is = System.in;
		}
		in = new FastScanner(is);
		out = new PrintWriter(System.out);

		Thread t = new Thread(null, new Runnable() {
			
			@Override
			public void run() {
				solve();
			}
		}, "lul", 1 << 30);
		t.start();
	}

	public static void main(String[] args) {
		new Main().run();
	}

	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");

		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}

		System.out.println("----------------------------");
		System.out.println();
	}

	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}

	class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
			//stream = new FileInputStream(new File("dec.in"));

		}

		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();

			return array;
		}

		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();

			return array;
		}

		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();

			return array;
		}

		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}