Problem:
Score : 500 points

Problem Statement

Let N be a positive integer.

There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}).
Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.
Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').

Find the maximum possible score of a'.

Constraints

1 ≤ N ≤ 10^5

a_i is an integer.

1 ≤ a_i ≤ 10^9

Partial Score

In the test set worth 300 points, N ≤ 1000.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{3N}

Output

Print the maximum possible score of a'.

Sample Input 1

2
3 1 4 1 5 9

Sample Output 1

1

When a_2 and a_6 are removed, a' will be (3, 4, 1, 5), which has a score of (3 + 4) - (1 + 5) = 1.

Sample Input 2

1
1 2 3

Sample Output 2

-1

For example, when a_1 are removed, a' will be (2, 3), which has a score of 2 - 3 = -1.

Sample Input 3

3
8 2 2 7 4 6 5 3 8

Sample Output 3

5

For example, when a_2, a_3 and a_9 are removed, a' will be (8, 7, 4, 6, 5, 3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5.

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream> // cout, endl, cin
#include <string> // string, to_string, stoi
#include <vector> // vector
#include <algorithm> // min, max, swap, sort, reverse, lower_bound, upper_bound
#include <utility> // pair, make_pair
#include <tuple> // tuple, make_tuple
#include <cstdint> // int64_t, int*_t
#include <cstdio> // printf
#include <map> // map
#include <queue> // queue, priority_queue
#include <set> // set
#include <stack> // stack
#include <deque> // deque
#include <unordered_map> // unordered_map
#include <unordered_set> // unordered_set
#include <bitset> // bitset
#include <cctype> // isupper, islower, isdigit, toupper, tolower
#include <iomanip> // setprecision
#include <complex> // complex
#include <math.h> 
#include <climits> 
#include <assert.h>
#include <random>
#define rep(i,n) for(int i=0; i<(n); i++)
using namespace std;
using ll = long long;
using P = pair<int,int>;
constexpr ll INF = 1e18;
constexpr int inf = 1e9;
constexpr ll mod = 1000000007;
constexpr ll mod2 = 998244353;
const double PI = 3.1415926535897932384626433832795028841971;
const int dx[8] = {1, 0, -1, 0,1,1,-1,-1};
const int dy[8] = {0, 1, 0, -1,1,-1,1,-1};
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
// ---------------------------------------------------------------------------

int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int N;
  cin >> N;
  vector<int> A(N*3);
  for(int i=0; i<N*3; i++) cin >> A[i];

  priority_queue<int,vector<int>,greater<int>> pre;
  ll pre_sum = 0;
  for(int i=0; i<N; i++){
    pre_sum += A[i];
    pre.emplace(A[i]);
  }
  vector<ll> pre_S;
  pre_S.emplace_back(pre_sum);
  for(int i=N; i<2*N; i++){
    pre_sum += A[i];
    pre_sum -= pre.top();
    pre.pop();
    pre_S.emplace_back(pre_sum);
  }

  reverse(A.begin(),A.end());
  priority_queue<int> suf;
  ll suf_sum = 0;
  for(int i=0; i<N; i++){
    suf_sum += A[i];
    suf.emplace(A[i]);
  }
  vector<ll> suf_S;
  suf_S.emplace_back(suf_sum);
  for(int i=N; i<2*N; i++){
    suf_sum += A[i];
    suf_sum -= suf.top();
    suf.pop();
    suf_S.emplace_back(suf_sum);
  }
  ll ans = -INF;
  reverse(suf_S.begin(),suf_S.end());
  for(int i=0; i<=N; i++){
    chmax(ans,pre_S[i]-suf_S[i]);
  }
  cout << ans << "\n";
  return 0;
}