Boredom

Posted 2021-02-09 clb123

Alex doesn‘t like boredom. That‘s why whenever he gets bored, he comes up with games. One long winter evening he came up with a game and decided to play it.

Given a sequence a consisting of n integers. The player can make several steps. In a single step he can choose an element of the sequence (let‘s denote it a_k) and delete it, at that all elements equal to a_k + 1 and a_k - 1 also must be deleted from the sequence. That step brings a_k points to the player.

Alex is a perfectionist, so he decided to get as many points as possible. Help him.

Input

The first line contains integer n (1 ≤ n ≤ 10⁵) that shows how many numbers are in Alex‘s sequence.

The second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁵).

Output

Print a single integer — the maximum number of points that Alex can earn.

Examples

Input

2
1 2

Output

2

Input

3
1 2 3

Output

4

Input

9
1 2 1 3 2 2 2 2 3

Output

10

Note

Consider the third test example. At first step we need to choose any element equal to 2. After that step our sequence looks like this [2, 2, 2, 2]. Then we do 4 steps, on each step we choose any element equals to 2. In total we earn 10 points.

 

 

题意：

给定一个序列，每次从序列中选出一个数ak,获得ak的得分，同时删除序列中所有的ak−1,ak+1,

求最大得分的值。

dp[i]=max(dp[i-2]+n[i]*i，dp[i-1])
dp[i]表示的是前i个的最大值，对于第i个有取和不取的情况，对于可以取到i的情况，删掉的一定是i-1这个点，剩下的就是前i-2的情况了，由于dp[i-2]包括了取i-2的情况，于是就不用再重复考虑i-2也要加一遍的情况了，然后再考虑不取i的情况，就不用考虑i了，于是就是dp[i-1]了

 

 

#include<bits/stdc++.h>
using namespace std;
const int N = 1e6+1;
long long num[N],dp[N];
int main()
{
    int n,a,i;
    cin>>n;
    int maxa=-1;
    int mina=N;
    for(i=0;i<n;i++){
        cin>>a;
        num[a]++;
        maxa = max(a,maxa);
        mina = min(a,mina);
    }
    dp[mina] = num[mina]*mina;
    for(i=mina+1; i <= maxa; i++){
        dp[i] = max(dp[i-2]+num[i]*i,dp[i-1]);
    }
    cout<<dp[maxa]<<endl;
    return 0;
}