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 12.16.1) (judge verdict: Accepted)

"use strict"
const create = () => {
    const input = require("fs").readFileSync("/dev/stdin", "utf8").trim().split("\n");
    const res = {
        "list": input, "index": 0, "max": input.length,
        "hasNext": function() {return this.index < this.max},
        "next": function() { if (!this.hasNext()) {throw "ArrayIndexOutOfBoundsException";}else{return this.list[this.index++];}}
    };
    return res;
}
const o = create();
const next = () => o.next()
const nextInt = () => parseInt(o.next())
const nextStrArray = () => o.next().split(" ")
const nextIntArray = () => o.next().split(" ").map(el => parseInt(el))
const nextCharArray = () => o.next().split("")
const hasNext = () => o.hasNext()
const myout = (...x) => console.log(...x)
const Main = () => {
    const n = nextInt()
    const a = nextIntArray()
    let m = {}
    let maxVal = 0
    for(let val of a){
        if(!m[val]) m[val] = 1
        else m[val]++
        maxVal = Math.max(maxVal, val)
    }
    let cnt = {}

    for(let i = 0; i<= maxVal; i++){
        let curr = m[i] ? m[i] : 0
        let prev = m[i-1]? m[i-1] : 0
        let next = m[i+1]? m[i+1] : 0
        cnt[i] = curr + prev + next
    }
    let ans = 1
    for(let key of Object.keys(cnt)){
        ans = Math.max(ans, cnt[key])
    }
    console.log(ans)
}
Main()