Problem: 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.

Examples

Input

2
1 2 1 2 2 1


Output

2


Input

3
1 1 2 2 3 3 3 2 1


Output

1


Input

3
1 1 2 2 2 3 3 3 1


Output

3

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class Main {
    static In in = new In();
    static Out out = new Out();
    static final long inf = 0x1fffffffffffffffL;
    static final int iinf = 0x3fffffff;
    static final double eps = 1e-9;
    static long mod = 1000000007;

    void solve() {
        int n = in.nextInt();
        int[] p = in.nextIntArray(n * 3);
        for (int i = 0; i < n * 3; i++) {
            p[i]--;
        }
        int[] dp = new int[n * n];
        int base = 0;
        int max = 0;
        int[] xMax = new int[n];
        for (int i = 0; i < n; i++) {
            xMax[i] = -iinf;
            for (int j = 0; j < n; j++) {
                dp[i * n + j] = -iinf;
            }
        }
        dp[p[0] * n + p[1]] = 0;
        dp[p[1] * n + p[0]] = 0;
        xMax[p[0]] = 0;
        xMax[p[1]] = 0;
        for (int i = 0; i < n - 1; i++) {
            if (p[i * 3 + 2] == p[i * 3 + 3] && p[i * 3 + 3] == p[i * 3 + 4]) {
                base++;
                continue;
            }
            List<IntPair> changes = new ArrayList<>();
            int oldMax = max;
            int[] oldXMax = Arrays.copyOf(xMax, n);
            for (int j = 0; j < 3; j++) {
                int a = p[i * 3 + 2 + (0 + j) % 3];
                int b = p[i * 3 + 2 + (1 + j) % 3];
                int c = p[i * 3 + 2 + (2 + j) % 3];
                if (a == b) {
                    for (int k = 0; k < n; k++) {
                        int v = Math.max(Math.max(dp[k * n + c], dp[c * n + k]), Math.max(dp[a * n + k], dp[k * n + a]) + 1);
                        changes.add(new IntPair(k * n + c, v));
                        changes.add(new IntPair(c * n + k, v));
                        max = Math.max(max, v);
                        xMax[k] = Math.max(xMax[k], v);
                        xMax[c] = Math.max(xMax[c], v);
                    }
                }
                int v = Math.max(oldMax, dp[c * n + c] + 1);
                changes.add(new IntPair(a * n + b, v));
                changes.add(new IntPair(b * n + a, v));
                max = Math.max(max, v);
                xMax[a] = Math.max(xMax[a], v);
                xMax[b] = Math.max(xMax[b], v);
                for (int k = 0; k < n; k++) {
                    changes.add(new IntPair(k * n + a, oldXMax[k]));
                    changes.add(new IntPair(a * n + k, oldXMax[k]));
                    xMax[k] = Math.max(xMax[k], oldXMax[k]);
                    xMax[a] = Math.max(xMax[a], oldXMax[k]);
                }
            }
            for (IntPair change : changes) {
                dp[change.first] = Math.max(dp[change.first], change.second);
            }
        }
        dp[p[n * 3 - 1] * (n + 1)]++;
        out.println(base + Math.max(dp[p[n * 3 - 1] * (n + 1)], max));
    }

    public static void main(String[]$) {
        new Main().solve();
        out.flush();
    }
}

class IntPair implements Comparable<IntPair> {
    int first;
    int second;

    IntPair(int first, int second) {
        this.first = first;
        this.second = second;
    }

    @Override
    public boolean equals(Object o) {
        if (!(o instanceof IntPair)) {
            return false;
        }
        IntPair that = (IntPair)o;
        return first == that.first && second == that.second;
    }

    @Override
    public int hashCode() {
        return first * 31 + second;
    }

    @Override
    public int compareTo(IntPair o) {
        return first == o.first ? Integer.compare(second, o.second) : Integer.compare(first, o.first);
    }

    @Override
    public String toString() {
        return String.format("[%s, %s]", first, second);
    }
}

class In {
    private BufferedReader reader = new BufferedReader(new InputStreamReader(System.in), 0x10000);
    private StringTokenizer tokenizer;

    String next() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
        } catch (IOException ignored) {
        }
        return tokenizer.nextToken();
    }

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

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

    char[] nextCharArray() {
        return next().toCharArray();
    }

    char[][] nextCharGrid(int n, int m) {
        char[][] a = new char[n][m];
        for (int i = 0; i < n; i++) {
            a[i] = next().toCharArray();
        }
        return a;
    }

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

    int[] nextIntArray(int n, IntUnaryOperator op) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsInt(nextInt());
        }
        return a;
    }

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

    long[] nextLongArray(int n, LongUnaryOperator op) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsLong(nextLong());
        }
        return a;
    }

    List<List<Integer>> nextEdges(int n, int m) {
        List<List<Integer>> res = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            res.add(new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            int u = nextInt() - 1;
            int v = nextInt() - 1;
            res.get(u).add(v);
            res.get(v).add(u);
        }
        return res;
    }
}

class Out {
    private PrintWriter out = new PrintWriter(System.out);
    boolean autoFlush = false;

    void println(Object... a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (Object obj : a) {
            joiner.add(String.valueOf(obj));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(char[] s) {
        out.println(String.valueOf(s));
        if (autoFlush) {
            out.flush();
        }
    }

    void println(int[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (int i : a) {
            joiner.add(Integer.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(long[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (long i : a) {
            joiner.add(Long.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void flush() {
        out.flush();
    }
}