mean bsp pri nts HERE move elves per desc

time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output

Two players A and B have a list of $\mathrm{nn\; integers\; each.\; They\; both\; want\; to\; maximize\; the\; subtraction\; between\; their\; score\; and\; their\; opponent‘s\; score.}$

In one turn, a player can either add to his score any element from his list (assuming his list is not empty), the element is removed from the list afterward. Or remove an element from his opponent‘s list (assuming his opponent‘s list is not empty).

Note, that in case there are equal elements in the list only one of them will be affected in the operations above. For example, if there are elements $\{1,2,2,3\}\{1,2,2,3\}\; in\; a\; list\; and\; you\; decided\; to\; choose\; 22\; for\; the\; next\; turn,\; only\; a\; single\; instance\; of\; 22\; will\; be\; deleted\; (and\; added\; to\; the\; score,\; if\; necessary).$

The player A starts the game and the game stops when both lists are empty. Find the difference between A‘s score and B‘s score at the end of the game, if both of the players are playing optimally.

Optimal play between two players means that both players choose the best possible strategy to achieve the best possible outcome for themselves. In this problem, it means that each player, each time makes a move, which maximizes the final difference between his score and his opponent‘s score, knowing that the opponent is doing the same.

Input

The first line of input contains an integer $\mathrm{nn\; (1\le n\le 1000001\le n\le 100000)\; —\; the\; sizes\; of\; the\; list.}$

The second line contains $\mathrm{nn\; integers\; aiai\; (1\le ai\le 1061\le ai\le 106),\; describing\; the\; list\; of\; the\; player\; A,\; who\; starts\; the\; game.}$

The third line contains $\mathrm{nn\; integers\; bibi\; (1\le bi\le 1061\le bi\le 106),\; describing\; the\; list\; of\; the\; player\; B.}$

Output

Output the difference between A‘s score and B‘s score ($\mathrm{A?BA?B)\; if\; both\; of\; them\; are\; playing\; optimally.}$

Examples input Copy

2
1 4
5 1

output Copy

0

input Copy

3
100 100 100
100 100 100

output Copy

0

input Copy

2
2 1
5 6

output Copy

-3

Note

In the first example, the game could have gone as follows:

• A removes $\mathrm{55\; from\; B‘s\; list.}$
• B removes $\mathrm{44\; from\; A‘s\; list.}$
• A takes his $11.$
• B takes his $11.$

Hence, A‘s score is $\mathrm{11,\; B‘s\; score\; is\; 11\; and\; difference\; is\; 00.}$

There is also another optimal way of playing:

• A removes $\mathrm{55\; from\; B‘s\; list.}$
• B removes $\mathrm{44\; from\; A‘s\; list.}$
• A removes $\mathrm{11\; from\; B‘s\; list.}$
• B removes $\mathrm{11\; from\; A‘s\; list.}$

The difference in the scores is still $00.$

In the second example, irrespective of the moves the players make, they will end up with the same number of numbers added to their score, so the difference will be $00.$

$\mathrm{題目大意：有A,B兩個競賽者各自擁有一個序列，他們可以在每一個回合中進行兩種操作，第一種操作是在對方的序列中刪除一個元素，第二種操作是把自己序列中的一個元素加入自己的得分中，A,B都想要自己的得分較高，輸出A-B的值。}$

$\mathrm{思路：將兩個序列排序，進行操作模擬。}$

#include <cstdio>
#include <iostream>
#include <string.h>
#include <queue>
#include <algorithm>
using namespace std;
int a[100010];
int b[100010];

int main()
{
    int n;
    scanf("%d",&n);
    for(int i=0; i<n; i++)
        scanf("%d",&a[i]);
    for(int i=0; i<n; i++)
        scanf("%d",&b[i]);
    sort(a,a+n);
    sort(b,b+n);
    long long sum=0;
    int t=0;
    int x=n-1;
    int y=n-1;
    while(x>=0||y>=0)
    {
        if(t%2==0)
        {
            if(a[x]>b[y]) sum+=a[x],x--;
            else y--;
        }
        else
        {
            if(a[x]>=b[y]) x--;
            else sum-=b[y],y--;
        }
        t++;
    }
    printf("%I64d\n",sum);
    return 0;
}

codeforces 1038C. Gambling(思維，模擬)