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 Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

Const   fi      ='b.inp';
        fo      ='b.out';
        maxn    =100005;
var     n       :longint;
        a,b,l1,l2       :array[0..maxn]of  longint;
Procedure       Nhap;
Var     i,j     :longint;
begin
        //Assign(input,fi);reset(input);
        read(n);
        For i:=1 to 3*n do read(a[i]);
End;

Procedure       swap(var i,j:longint);
Var     tg      :longint;
Begin
        tg:=i;i:=j;j:=tg;
End;

Procedure       xl;
Var     i,j,vt  :Longint;
        res,kq  :int64;
Begin
        //assign(output,fo);Rewrite(output);
        For i:=1 to n do
        For j:=i+1 to n do
                if a[i]<a[j] then swap(a[i],a[j]);
        b[0]:=1000000005;res:=0;
        For i:=1 to n do
        begin
                res:=res+a[i];
                b[i]:=a[i];
        end;
        l1[n]:=res;
        For i:=n+1 to 2*n do
        begin
                b[n+1]:=a[i];
                vt:=n+1;
                while b[vt]>b[vt-1] do
                begin
                        swap(b[vt],b[vt-1]);
                        dec(vt);
                end;
                res:=res-b[n+1]+a[i];
                l1[i]:=res;
        end;
        For i:=2*n+1 to 3*n do
        For j:=i+1 to 3*n do
                if a[i]>a[j] then swap(a[i],a[j]);
        res:=0;b[0]:=-1000000005;
        For i:=1 to n do
        begin
                res:=res+a[i+2*n];
                b[i]:=a[i+2*n];
        end;
        l2[2*n+1]:=res;
        For i:=2*n downto n+1 do
        begin
                b[n+1]:=a[i];
                vt:=n+1;
                while b[vt]<b[vt-1] do
                begin
                        swap(b[vt],b[vt-1]);
                        dec(vt);
                end;
                res:=res+a[i]-b[n+1];
                l2[i]:=res;
        end;
        kq:=-1000000005;
        For i:=n to 2*n do
        For j:=i+1 to 2*n+1 do
                if kq<l1[i]-l2[j] then kq:=l1[i]-l2[j];
        write(kq);
End;

Begin
        Nhap;
        xl;
End.