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.util.*;
import java.math.*;
import java.io.*;
import java.text.*;

public class A{
	
static class Node implements Comparable<Node> {
	int x;
	int y;
	public Node(int x,int y) {
		this.x=x;
		this.y=y;
	}
	public int compareTo(Node c) {
	   return this.y-c.y;	
	}
}
static class Pair implements Comparable<Pair>{
	int x;
	int y;
	long cnt;
	public Pair(int x,int y,long cnt) {
		this.x=x;
		this.y=y;
		this.cnt=cnt;
	}
	public int compareTo(Pair c) {
		int i=Long.compare(this.cnt, c.cnt);
		if(i!=0)return i;
		i=Long.compare(this.x+this.y, c.x+c.y);
		return i;
	}
}
//public static PrintWriter pw; 
public static PrintWriter pw=new PrintWriter(System.out);
public static void solve() throws IOException{
//	pw=new PrintWriter(new FileWriter("C:\\Users\\shree\\Downloads\\small_output_in"));
	FastReader sc=new FastReader();
	int n=sc.I();
	int a[]=new int[n+1];
	for(int i=1;i<=n;i++)a[i]=sc.I();
	int prev1[]=new int[100005];
	int prev2[]=new int[8];
	int dp[][]=new int[n+1][n+1];
	for(int i=n-1;i>=1;i--) {
		for(int j=i;j<=n;j++)prev1[a[j]]=prev2[a[j]%7]=0;
		for(int j=n;j>i;j--) {
			
			if(prev1[a[j]+1]!=0) dp[i][j]=Math.max(dp[i][j],1+dp[i][prev1[a[j]+1]]);
			if(prev1[a[j]-1]!=0) dp[i][j]=Math.max(dp[i][j], 1+dp[i][prev1[a[j]-1]]);
			if(prev2[a[j]%7]!=0) dp[i][j]=Math.max(dp[i][j],1+dp[i][prev2[a[j]%7]]);
			if(prev1[a[i]+1]!=0) dp[i][j]=Math.max(dp[i][j], 1+dp[j][prev1[a[i]+1]]);
			if(prev1[a[i]-1]!=0) dp[i][j]=Math.max(dp[i][j], 1+dp[j][prev1[a[i]-1]]);
			if(prev2[a[i]%7]!=0) dp[i][j]=Math.max(dp[i][j], 1+dp[j][prev2[a[i]%7]]);
			prev1[a[j]]=j;
			prev2[a[j]%7]=j;
			
		}
	
	}
	Arrays.fill(prev1, 0);
	Arrays.fill(prev2, 0);
	int dp2[]=new int[n+1];
	int ans=0;
    for(int i=1;i<=n-1;i++){

    	dp2[i] = 1;
    	if(prev1[a[i]-1] != 0)	dp2[i] = Math.max(dp2[i], 1 + dp2[prev1[a[i]-1]]);
    	if(prev1[a[i]+1] != 0)	dp2[i] = Math.max(dp2[i], 1 + dp2[prev1[a[i]+1]]);
    	if(prev2[a[i]%7] != 0)	dp2[i] = Math.max(dp2[i], 1 + dp2[prev2[a[i]%7]]);

    	prev1[a[i]] = i;
    	prev2[a[i]%7] = i;

    	for(int j=i+1;j<=n;j++)
    		ans = Math.max(ans, dp2[i]+1+dp[i][j]);
    }
	
/*	for(int i=n;i>=1;i--) {
		for(int j=i+1;j<=n;j++) {
			pw.print(dp[i][j]+" ");
			
		}
		pw.println("");
	}*/
	pw.println(ans);
	
	pw.close(); 
	
}

public static void main(String[] args)  {
    new Thread(null ,new Runnable(){
      public void run(){
          try{
          
              solve();
          } catch(Exception e){
              e.printStackTrace();
          }
      }
  },"1",1<<26).start();
 
}

static long M=(long)Math.pow(10,9)+7;
 
	static class FastReader {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader() throws FileNotFoundException{
            //br=new BufferedReader(new FileReader("C:\\Users\\shree\\Downloads\\B-small-practice.in"));	
        	 br = new BufferedReader(new InputStreamReader(System.in));
        		
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
       
        int I(){   return Integer.parseInt(next()); }
        long L(){  return Long.parseLong(next()); }
        double D() {  return Double.parseDouble(next()); }
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
     }
}