Problem:
Score : 600 points

Problem Statement

We have 3N cards arranged in a row from left to right, where each card has an integer between 1 and N (inclusive) written on it. The integer written on the i-th card from the left is A_i.

You will do the following operation N-1 times:

Rearrange the five leftmost cards in any order you like, then remove the three leftmost cards. If the integers written on those three cards are all equal, you gain 1 point.

After these N-1 operations, if the integers written on the remaining three cards are all equal, you will gain 1 additional point.

Find the maximum number of points you can gain.

Constraints

1 \leq N \leq 2000

1 \leq A_i \leq N

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_{3N}

Output

Print the maximum number of points you can gain.

Sample Input 1

2
1 2 1 2 2 1

Sample Output 1

2

Let us rearrange the five leftmost cards so that the integers written on the six cards will be 2\ 2\ 2\ 1\ 1\ 1 from left to right.

Then, remove the three leftmost cards, all of which have the same integer 2, gaining 1 point.

Now, the integers written on the remaining cards are 1\ 1\ 1.

Since these three cards have the same integer 1, we gain 1 more point.

In this way, we can gain 2 points - which is the maximum possible.

Sample Input 2

3
1 1 2 2 3 3 3 2 1

Sample Output 2

1

Sample Input 3

3
1 1 2 2 2 3 3 3 1

Sample Output 3

3

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedOutputStream;
import java.io.UncheckedIOException;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        FBraveCHAIN solver = new FBraveCHAIN();
        solver.solve(1, in, out);
        out.close();
    }

    static class FBraveCHAIN {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            int n = in.ints();
            int[] a = new int[3 * n];
            for (int i = 0; i < 3 * n; i++) a[i] = in.ints() - 1;
            int[][] dp = new int[n][n];
            ArrayUtil.fill(dp, Integer.MIN_VALUE);
            dp[a[0]][a[1]] = dp[a[1]][a[0]] = 0;
            int all = 0;
            int[] t = new int[3];
            int cur = 0, max = 0;
            int[] dx = new int[8 * n], dy = new int[8 * n], nv = new int[8 * n];
            for (int i = 1; i < n; i++) {
                cur = 0;
                t[0] = a[3 * i - 1];
                t[1] = a[3 * i];
                t[2] = a[3 * i + 1];
                Arrays.sort(t);
                if (t[0] == t[2]) {
                    all++;
                    continue;
                }
                for (int j = 0; j < 3; j++) {
                    for (int o1 = 0; o1 < n; o1++) {
                        dx[cur] = t[j];
                        dy[cur] = o1;
                        nv[cur++] = max;
                    }
                }
                for (int j = 0; j < 3; j++) {
                    int o1 = t[(j + 1) % 3], o2 = t[(j + 2) % 3];
                    dx[cur] = o1;
                    dy[cur] = o2;
                    nv[cur++] = dp[t[j]][t[j]] + 1;
                    dx[cur] = o1;
                    dy[cur] = o2;
                    nv[cur++] = max;
                }
                for (int j = 0; j < 3; j++) {
                    int s1 = t[(j + 1) % 3], s2 = t[(j + 2) % 3];
                    if (s1 != s2) continue;
                    int o1 = t[j];
                    for (int o2 = 0; o2 < n; o2++) {
                        dx[cur] = o1;
                        dy[cur] = o2;
                        nv[cur++] = dp[s1][o2] + 1;
                    }
                }
                for (int j = 0; j < cur; j++) {
                    dp[dx[j]][dy[j]] = Math.max(dp[dx[j]][dy[j]], nv[j]);
                    dp[dy[j]][dx[j]] = Math.max(dp[dy[j]][dx[j]], nv[j]);
                    max = Math.max(max, nv[j]);
                }
            }
            int ans = 0, last = a[3 * n - 1];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (dp[i][j] != dp[j][i]) throw new RuntimeException();
                    if (i == last && j == last) ans = Math.max(ans, dp[i][j] + 1);
                    else ans = Math.max(ans, dp[i][j]);
                }
            }
            out.ans(ans + all).ln();
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new OutputStreamWriter(new BufferedOutputStream(out), Charset.defaultCharset()));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(int i) {
            return ans(Integer.toString(i));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class LightScanner implements AutoCloseable {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public void close() {
            try {
                this.reader.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static final class ArrayUtil {
        private ArrayUtil() {
        }

        public static void fill(int[] a, int v) {
            Arrays.fill(a, v);
        }

        public static void fill(int[][] a, int v) {
            for (int i = 0; i < a.length; i++) {
                fill(a[i], v);
            }
        }

    }
}