CodeForces-455A Boredom

题目链接

https://vjudge.net/problem/CodeForces-455A

题面

Description

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 + 1 and 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 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.

题解

简单DP题，记录一下每个数有多少个，\(dp[i]\)表示消除值为i的数字或者不消除值为i的数字的最大分数，直接从最小的数字的值开始dp是否消除即可

AC代码

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define N 100050
using namespace std;
long long f[N];
long long cnt[N];
bool vis[N];
long long a[N];
int main() {
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        scanf("%lld", &a[i]);
    }
    sort (a + 1, a + n + 1);
    for (int i = 1; i <= n; i++) {
        cnt[a[i]]++;
    }
    long long ans = 0;
    for (int i = a[1]; i <= a[n]; i++) {
        f[i] = max(f[i - 1], f[i - 2] + cnt[i] * i);
        ans = max(ans, f[i]);
    }
    printf("%lld\n", ans);
    return 0;
}