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.util.Arrays;

public class Main {

	public static void main(String[] args) {
	    java.util.Scanner scanner = new java.util.Scanner(System.in);
	    int n = scanner.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = scanner.nextInt();
		}
		Arrays.sort(a);
		int count1 = 1;
		int count2 = 0;
		int count3 = 0;
		int maxcount = 1;
		// 1 1 2 2 3 3
		for (int i = 0; i < n - 1; i++) {
			maxcount = Math.max(maxcount, count1+count2+count3);
			int diff = a[i+1] - a[i];
			if (diff == 0) {
				count1++;
			} else if (diff == 1) {
				count3 = count2;
				count2 = count1;
				count1 = 1;
			} else {
				count3 = 0;
				count2 = 0;
				count1 = 1;
				// reset
			}
		}
//		if (n > 1) {
//			int lastdiff = a[n - 1] - a[n - 2];
//			if (lastdiff == 0) {
//				count1++;
//			} else if (lastdiff == 1) {
//				count3 = count2;
//				count2 = count1;
//				count1 = 1;
//			} else {
//				count3 = 0;
//				count2 = 0;
//				count1 = 1;
//			}
//			maxcount = Math.max(maxcount, count1+count2+count3);
//		}
		maxcount = Math.max(maxcount, count1+count2+count3);
		System.out.println(maxcount);
	}
}