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cf455A boredom

时间:2019-11-13 22:31:01      阅读:59      评论:0      收藏:0      [点我收藏+]

标签:turn   set   ++   play   class   game   contain   i+1   tle   

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 ak) and delete it, at that all elements equal to ak + 1and ak - 1 also must be deleted from the sequence. That step brings ak 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 a1a2, ..., an (1 ≤ ai ≤ 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.

 

思路:dp。就是表示每一步dp的状态,即此步状态可能是前一步dp[i-1]的状态(即这一步的数已被消除),或者是前两步dp[i-2]的状态加上这一步的值(因为下一步的状态不确定,所以下一步的值不能消去)。

所以状态转移方程就是dp[i] = max(dp[i-2] + a[i]*i,dp[i-1]);

#include<bits/stdc++.h>
using namespace std;
const int N = 1e5+10;
typedef long long ll;
ll a[N],dp[N];
int main()
{
    int n,x,ma = 0,mi = N;
    memset(a,0,sizeof(a));
    memset(dp,0,sizeof(dp));
    cin>>n;
    for(ll i = 0; i < n; i++) {
        scanf("%d",&x);
        a[x]++;
        if(x > ma) {
            ma = x;
        }
        if(x < mi) {
            mi = x;
        }
    }
    dp[mi] = a[mi]*mi;
    for(ll i = mi+1; i <= ma; i++) {
        dp[i] = max(dp[i-2]+a[i]*i,dp[i-1]);
    }
    cout<<dp[ma]<<endl;
    return 0;
}

  

cf455A boredom

标签:turn   set   ++   play   class   game   contain   i+1   tle   

原文地址:https://www.cnblogs.com/clb123/p/11853280.html

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