Problem: Author note: I think some of you might remember the problem "Two Melodies" from Eductational Codeforces Round 22. Now it's time to make it a bit more difficult!

Alice is a composer, and recently she had recorded two tracks that became very popular. Now she has got a lot of fans who are waiting for new tracks. 

This time Alice wants to form four melodies for her tracks.

Alice has a sheet with n notes written on it. She wants to take four such non-empty non-intersecting subsequences that all of them form a melody and sum of their lengths is maximal.

Subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

Subsequence forms a melody when each two adjacent notes either differ by 1 or are congruent modulo 7.

You should write a program which will calculate maximum sum of lengths of such four non-empty non-intersecting subsequences that all of them form a melody.

Input

The first line contains one integer number n (4 ≤ n ≤ 3000).

The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105) — notes written on a sheet.

Output

Print maximum sum of lengths of such four non-empty non-intersecting subsequences that all of them form a melody.

Examples

Input

5
1 3 5 7 9


Output

4


Input

5
1 3 5 7 2


Output

5

Note

In the first example it is possible to compose 4 melodies by choosing any 4 notes (and each melody will consist of only one note).

In the second example it is possible to compose one melody with 2 notes — {1, 2}. Remaining notes are used in other three melodies (one note per each melody).

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class TaskD {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = new int[n + 2];
            int[] rem = new int[n + 2];
            for (int i = 0; i < n; i++) {
                a[i + 2] = in.nextInt();
                rem[i + 2] = a[i + 2] % 7;
            }
            n += 2;
            int[][] cand = new int[n][9];
            int[] numCand = new int[n];
            for (int i = n - 1; i >= 0; i--) {
                int x = 0;
                int y = 0;
                int z = 0;
                if (i > 1) {
                    for (int j = i + 1; j < n; j++) {
                        if (x < 3 && a[i] + 1 == a[j]) {
                            cand[i][numCand[i]++] = j;
                            ++x;
                        } else if (y < 3 && a[i] - 1 == a[j]) {
                            cand[i][numCand[i]++] = j;
                            ++y;
                        } else if (z < 3 && rem[i] == rem[j]) {
                            cand[i][numCand[i]++] = j;
                            ++z;
                        }
                    }
                } else {
                    cand[i] = new int[n];
                    for (int j = 2; j < n; j++) {
                        cand[i][numCand[i]++] = j;
                    }
                }
            }
            for (int i = 0; i < cand.length; i++) {
                cand[i] = Arrays.copyOf(cand[i], numCand[i]);
            }
            int[][] d = new int[n][n];
            int ans = 0;
            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    ans = Math.max(ans, d[i][j]);
                    for (int ni : cand[i]) {
                        if (ni > j) {
                            d[j][ni] = Math.max(d[j][ni], 1 + d[i][j]);
                        }
                    }
                    for (int nj : cand[j]) {
                        d[i][nj] = Math.max(d[i][nj], 1 + d[i][j]);
                    }
                }
            }
            out.println(ans);
        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

    }
}