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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func main() {
	sc.Split(bufio.ScanWords)
	n := nextInt()
	nums := map[int]int{}

	for i := 0; i < n; i++ {
		val := nextInt()

		if _, ok := nums[val]; ok {
			nums[val]++
		} else {
			nums[val] = 1
		}

		if _, ok := nums[val+1]; ok {
			nums[val+1]++
		} else {
			nums[val+1] = 1
		}

		if _, ok := nums[val-1]; ok {
			nums[val-1]++
		} else {
			nums[val-1] = 1
		}
	}

	max := 0
	for _, v := range nums {
		if max < v {
			max = v
		}
	}
	fmt.Println(max)
}