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++14 (GCC 5.4.1) (judge verdict: Accepted)


#include <algorithm>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
//#include <regex>

/* g++ -g -std=c++0x */
/* g++ -g -std=c++11 */

using namespace std;

// std::ios::sync_with_stdio(false);

// freopen("input.txt", "rt", stdin);
// freopen("output.txt", "wt", stdout);

#define ALL(c)          (c).begin(), (c).end()
#define ALLR(c)         (c).rbegin(), (c).rend()
#define FOR(i,a,b)      for (int i=(a); i < (b); ++i)
#define FORR(i,a,b)     for (int i=(a); i > (b); --i)
#define FOR_ALL(i,c)    for (__typeof((c).begin()) i=(c).begin();   \
                             i != (c).end(); ++i)
#define FOR_ALLR(i,c)   for (__typeof((c).rbegin()) i=(c).rbegin(); \
                             i != (c).rend(); ++i)
#define SZ(array)       (sizeof(array)/sizeof(array[0]))
#define lc(x)           (x<<1)     /* 2*x */
#define rc(x)           (x<<1 | 1) /* 2*x+1 */
#define lowbit(x)       (x & (-x)) /* 0b10100 -> 0b100 */

typedef long long       LL;
typedef map<int,int>    MII;
typedef pair<int,int>   PII;
typedef set<int>        SI;
typedef vector<bool>    VB;
typedef vector<double>  VD;
typedef vector<int>     VI;
typedef vector<string>  VS;

/* check if a key is in container C */
template <class C>
inline bool in_(const typename C::key_type& k, const C& A)
{ return A.find(k) != A.end(); }
inline bool in_(const string& s, const string& S)
{ return S.find(s) != string::npos; }

int main()
{
    /* #ifndef ONLINE_JUDGE */
    /*     freopen("foo", "rt", stdin); */
    /* #endif */
    int N;
    while (cin >> N) {
        map<int,int> seq;
        FOR(i,0,N) {
            int x; cin >> x;
            seq[x]++;
        }
        int ans = 1;
        FOR_ALL(i,seq) {
            const int X = i->first;
            int res = i->second;
            auto j = i; 
            if (j != seq.begin()) {
                --j;
                const int xx = X - (j->first);
                if (xx <= 1)
                    res += j->second;
                ++j;
            }
            ++j;
            if (j != seq.end()) {
                const int xx = (j->first) - X;
                if (xx <= 1)
                    res += j->second;
            }
            ans = max(ans,res);
        }
        cout << ans << endl;
    }
    return 0;
}