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: Time Limit Exceeded)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.util.stream.LongStream;
import java.util.Collection;
import java.io.IOException;
import java.util.Random;
import java.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.util.stream.Stream;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 * 
 * @author daltao
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "daltao", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            TaskE solver = new TaskE();
            solver.solve(1, in, out);
            out.close();
        }
    }
    static class TaskE {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();

            Rect[] rects = new Rect[n];
            List<Long> summary = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                rects[i] = new Rect();
                for (int j = 0; j < 4; j++) {
                    rects[i].colors[j] = in.readInt();
                }
                long s = summaryOf(rects[i]);
                for (int j = 0; j < 4; j++) {
                    summary.add(s);
                    s = rotate(s);
                }
            }

            LongDiscreteMap dm = new LongDiscreteMap(summary.stream().mapToLong(Long::longValue).toArray(), 0,
                            summary.size());

            int[][] rotations = new int[dm.maxRank() + 1][4];
            for (int i = 0; i < rotations.length; i++) {
                long val = dm.iThElement(i);
                for (int j = 0; j < 4; j++) {
                    rotations[i][j] = dm.rankOf(val);
                    val = rotate(val);
                }
            }

            int[] cnts = new int[dm.maxRank() + 1];
            for (Rect rect : rects) {
                rect.summary = dm.rankOf(summaryOf(rect));
                for (int s : rotations[rect.summary]) {
                    cnts[s] += 1;
                }
            }

            int[] cols = new int[8];
            int[] faces = new int[3];

            long cnt = 0;

            Randomized.randomizedArray(rects, 0, n);
            for (int i = 0; i < n; i++) {
                for (int s : rotations[rects[i].summary]) {
                    cnts[s] -= 1;
                }
                cols[0] = rects[i].get(0, 0);
                cols[1] = rects[i].get(3, 0);
                cols[2] = rects[i].get(1, 0);
                cols[3] = rects[i].get(2, 0);

                for (int j = i + 1; j < n; j++) {
                    if (i == j) {
                        continue;
                    }

                    for (int s : rotations[rects[j].summary]) {
                        cnts[s] -= 1;
                    }

                    for (int rj = 0; rj < 4; rj++) {

                        if (rects[j].get(0, rj) != cols[2] || rects[j].get(3, rj) != cols[3]) {
                            continue;
                        }

                        cols[4] = rects[j].get(1, rj);
                        cols[5] = rects[j].get(2, rj);

                        for (int k = i + 1; k < n; k++) {
                            if (k == i || k == j) {
                                continue;
                            }


                            for (int rk = 0; rk < 4; rk++) {

                                if (rects[k].get(0, rk) != cols[4] || rects[k].get(3, rk) != cols[5]) {
                                    continue;
                                }

                                cols[6] = rects[k].get(1, rk);
                                cols[7] = rects[k].get(2, rk);

                                for (int s : rotations[rects[k].summary]) {
                                    cnts[s] -= 1;
                                }

                                faces[0] = dm.rankOf(summaryOf(cols[6], cols[0], cols[1], cols[7]));
                                faces[1] = dm.rankOf(summaryOf(cols[7], cols[1], cols[3], cols[5]));
                                faces[2] = dm.rankOf(summaryOf(cols[0], cols[6], cols[4], cols[2]));

                                if (faces[0] >= 0 && faces[1] >= 0 && faces[2] >= 0) {
                                    long localCnt = 1;
                                    for (int t = 0; t < 3; t++) {
                                        localCnt *= cnts[faces[t]];
                                        for (int r : rotations[faces[t]]) {
                                            cnts[r]--;
                                        }
                                    }
                                    cnt += localCnt;
                                    for (int t = 0; t < 3; t++) {
                                        for (int r : rotations[faces[t]]) {
                                            cnts[r]++;
                                        }
                                    }
                                }

                                for (int s : rotations[rects[k].summary]) {
                                    cnts[s] += 1;
                                }

                            }
                        }
                    }

                    for (int s : rotations[rects[j].summary]) {
                        cnts[s] += 1;
                    }
                }
            }

            out.println(cnt);
        }

        public long summaryOf(Rect rect) {
            return summaryOf(rect.colors[0], rect.colors[1], rect.colors[2], rect.colors[3]);
        }

        public long summaryOf(int a, int b, int c, int d) {
            long ans = a;
            ans = ans * 1000 + b;
            ans = ans * 1000 + c;
            ans = ans * 1000 + d;
            return ans;
        }

        public long rotate(long x) {
            return (x % 1000) * 1_000_000_000 + x / 1000;
        }

    }
    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }
    static class Rect {
        int[] colors = new int[4];
        int summary;

        public int get(int i, int r) {
            return colors[(i + r) & 3];
        }

    }
    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(1 << 20);
        private final Writer os;

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput println(long c) {
            cache.append(c).append('\n');
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

    }
    static class LongDiscreteMap {
        long[] val;
        int f;
        int t;

        public LongDiscreteMap(long[] val, int f, int t) {
            Randomized.randomizedArray(val, f, t);
            Arrays.sort(val, f, t);
            int wpos = f + 1;
            for (int i = f + 1; i < t; i++) {
                if (val[i] == val[i - 1]) {
                    continue;
                }
                val[wpos++] = val[i];
            }
            this.val = val;
            this.f = f;
            this.t = wpos;
        }

        public int rankOf(long x) {
            return Arrays.binarySearch(val, f, t, x) - f;
        }

        public long iThElement(int i) {
            return val[f + i];
        }

        public int maxRank() {
            return t - f - 1;
        }

        public String toString() {
            return Arrays.toString(Arrays.copyOfRange(val, f, t));
        }

    }
    static class Randomized {
        static Random random = new Random();

        public static void randomizedArray(long[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                long tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static <T> void randomizedArray(T[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                T tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }
}