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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    const N = parseInt(arg[0]);
    const a = arg[1].split(" ").map(n=>parseInt(n)).sort((a,b)=>a-b);
    
    const set = new Set();
    
    let max = 0;
    
    for(let i=0; i<N; i++) {
        let cnt = 0;
        
        if(set.has(a[i])) {
            continue;
        }
        
        set.add(a[i]);
        
        for(let j=0; j<N; j++) {
            if(Math.abs(a[j] - a[i]) <= 1) {
                cnt++;
            }
        }
        
        if(cnt > max) {
            max = cnt;
        }
    }
    
    console.log(max);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));