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: Accepted)

"use strict"

function main(input) {
  input = input.split(/\s|\n/).map(v => ~~v)
  const nums = input.slice(1, -1)
  let nums2 = []
  for (let i = 0; i < nums.length; i++) {
    nums2.push(nums[i] - 1)
    nums2.push(nums[i])
    nums2.push(nums[i] + 1)
  }
  const nums3 = nums2.sort((a, b) => a - b)
  let ans = 1
  let tmpcnt = 1
  let tmp = Number.MAX_SAFE_INTEGER
  for (let i = 0; i < nums3.length; i++) {
    if (tmp == nums3[i]) {
      tmpcnt++
    } else {
      tmp = nums3[i]
      tmpcnt = 1
    }
    ans = Math.max(tmpcnt, ans)
  }
  console.log(ans)
}
main(require("fs").readFileSync("/dev/stdin", "utf8"))