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 C (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>

#define BUF_SIZE 1000000

int main(void) {
  char line[BUF_SIZE];
  FILE *fp = stdin;
  int num;
  if(!fgets(line, BUF_SIZE, fp)) return 0;
  sscanf(line, "%d", &num);

  if(!fgets(line, BUF_SIZE, fp)) return 0;
  char *tmpbuf = line;
  int i;
  int hist[100001] = {0};
  int ma = 0;
  int mi = 100001;
  for(i = 0; i < num; i++) {
    char *tmp = strtok(tmpbuf, " ");
    int n = strtol(tmp, NULL, 10);
    hist[n]++;
    if(n > ma) ma=n;
    if(n < mi) mi=n;
    tmpbuf = NULL;
  }
  int max = 0;
  for(i = mi; i <= ma; i++) {
    int change = hist[i];
    if(i-1>=0) change += hist[i-1];
    if(i+1<=100000) change += hist[i+1];
    if(change > max) max = change;
  }

  printf("%d\n", max);
  return 0;
}