Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length N, a_1,a_2,...,a_N.

For each 1≤i≤N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.

After these operations, you select an integer X and count the number of i such that a_i=X.

Maximize this count by making optimal choices.

Constraints

1≤N≤10^5

0≤a_i<10^5 (1≤i≤N)

a_i is an integer.

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N

Output

Print the maximum possible number of i such that a_i=X.

Sample Input 1

7
3 1 4 1 5 9 2

Sample Output 1

4

For example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.

Sample Input 2

10
0 1 2 3 4 5 6 7 8 9

Sample Output 2

3

Sample Input 3

1
99999

Sample Output 3

1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Map;
import java.util.stream.Stream;

public class Main {
    FastScanner in = new FastScanner(System.in);
    PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        new Main().calc();
    }
    
    public void calc() {
        int N = in.nextInt();
        int a[] = new int[N];

        for (int i = 0; i < N; i++) {
            a[i] = in.nextInt();
        }

        Map<Integer, Integer> map = new HashMap<Integer, Integer>();
        
        for (int i = 0; i < N; i++) {
            map.put(a[i], map.getOrDefault(a[i], 0) + 1);
            map.put(a[i] + 1, map.getOrDefault(a[i] + 1, 0) + 1);
            map.put(a[i] - 1, map.getOrDefault(a[i] - 1, 0) + 1);
        }

        int ans = 0;
        
        for (Map.Entry<Integer, Integer> e: map.entrySet()) {
            // out.println(e.getKey() + ", " + e.getValue());
            ans = Math.max(e.getValue(), ans);
        }
        
        out.println(ans);
        out.close();
    }
    
    class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastScanner(InputStream stream) {
            this.stream = stream;
        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

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

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

            return array;
        }

        int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextIntArray(m);
            }
            return map;
        }

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

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

            return array;
        }

        long[][] nextLongMap(int n, int m) {
            long[][] map = new long[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextLongArray(m);
            }
            return map;
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double[] nextDoubleArray(int n) {
            double[] array = new double[n];
            for (int i = 0; i < n; i++)
                array[i] = nextDouble();

            return array;
        }

        double[][] nextDoubleMap(int n, int m) {
            double[][] map = new double[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextDoubleArray(m);
            }
            return map;
        }

        String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        String[] nextStringArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++)
                array[i] = next();

            return array;
        }

        String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }
}