Problem:
Score : 500 points

Problem Statement

There are N children standing in a line from left to right. The activeness of the i-th child from the left is A_i.

You can rearrange these children just one time in any order you like.

When a child who originally occupies the x-th position from the left in the line moves to the y-th position from the left, that child earns A_x \times |x-y| happiness points.

Find the maximum total happiness points the children can earn.

Constraints

2 \leq N \leq 2000

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum total happiness points the children can earn.

Sample Input 1

4
1 3 4 2

Sample Output 1

20

If we move the 1-st child from the left to the 3-rd position from the left, the 2-nd child to the 4-th position, the 3-rd child to the 1-st position, and the 4-th child to the 2-nd position, the children earns 1 \times |1-3|+3 \times |2-4|+4 \times |3-1|+2 \times |4-2|=20 happiness points in total.

Sample Input 2

6
5 5 6 1 1 1

Sample Output 2

58

Sample Input 3

6
8 6 9 1 2 1

Sample Output 3

85

Solution in Pascal (FPC 3.0.4) (judge verdict: Time Limit Exceeded)

uses crt,math;
const   fi='';
        nmax=2000;
        vc=100000000;
type    data=int64;
var
        f:text;
        A:array[0..nmax+1,0..nmax+1] of data;
        Fx,Fy,MatchX,MatchY,tr:array[0..nmax+1] of data;
        Q:array[0..nmax*nmax] of data;
        ddx,ddy:array[0..nmax+1] of boolean;
        dau,cuoi,start,finish:data;
        n:longint;
        mm :data;

procedure docfile;
var     u,v,c:data;
        i,j:longint;
begin
        clrscr;
        readln(n);
        for i:=1 to n do
        begin
                read(u);
                for j:=1 to n do begin a[i,j] := u*abs(i-j); mm := max(mm,a[i,j]); end;
        end;
        for i:=1 to n do
        begin
                for j:=1 to n do a[i,j] := mm - a[i,j];
        end;
end;

procedure init;
var     i,j:longint;
begin
        fillchar(MatchX,sizeof(matchx),0);
        MatchY:=MatchX;

        for i:=1 to n do
                begin
                        fx[i]:=vc;
                        for j:=1 to n do
                                if fx[i]>a[i,j] then
                                        fx[i]:=a[i,j];
                end;
        for i:=1 to n do
                begin
                        fy[i]:=vc;
                        for j:=1 to n do
                                if a[i,j]-fx[i]<fy[i] then
                                        fy[i]:=a[i,j]-fx[i];
                end;
end;

function get(i,j:longint):data;
begin
        get:=a[i,j]-fx[i]-fy[j];
end;

procedure themvao(x:data);
begin
        inc(cuoi);
        q[cuoi]:=x;
end;

function layra:data;
begin
        layra:=q[dau];
        inc(dau);
end;

procedure bfs;
var     u,v,j,i:longint;
begin
        fillchar(tr,sizeof(tr),0);
        dau:=1;
        cuoi:=0;
        themvao(start);
        while dau<=cuoi do
                begin
                        u:=layra;
                        for v:=1 to n do
                                if (tr[v]=0) and (get(u,v)=0) then
                                        begin
                                                tr[v]:=u;
                                                if matchy[v]=0 then
                                                        begin
                                                                finish:=v;
                                                                exit;
                                                        end;
                                                themvao(matchy[v]);
                                        end;
                end;
end;

procedure enlager(u:longint);
var     v,next:longint;
begin
        repeat
                v:=tr[u];
                next:=MatchX[v];
                MatchX[v]:=u;
                MatchY[u]:=v;
                u:=next;
        until   u=0;
end;

procedure subX_addY;
var    delta:data;
        i,j:longint;
begin
        fillchar(ddx,sizeof(ddx),false);
        ddy:=ddx;
        ddx[start]:=true;
        for i:=1 to n do
                if tr[i]<>0 then
                        begin
                                ddx[MatchY[i]]:=true;
                                ddy[i]:=true;
                        end;
        delta:=vc;
        for i:=1 to n do
                if ddx[i] then
                        for j:=1 to n do
                                if (not ddy[j]) and (delta>get(i,j)) then
                                        delta:=get(i,j);
        for i:=1 to n do
                begin
                        if ddx[i] then fx[i]:=fx[i]+delta;
                        if ddy[i] then fy[i]:=fy[i]-delta;
                end;
end;

procedure xuli;
var     res:data;
        i,j:longint;
begin
        for i:=1 to n do
                begin
                        start:=i;
                        finish:=0;
                        repeat
                                bfs;
                                if finish=0 then subx_addy;
                        until finish<>0;
                        enlager(finish);
                end;
        res:=0;
        for i:=1 to n do
                if MatchX[i]<>0 then
                        inc(res,a[i,Matchx[i]]);
        writeln(mm*n - res);
        {for i:=1 to n do
                if MatchX[i]<>0 then
                        writeln(i, ' ',MatchX[i]);   }

end;

begin
        docfile;
        init;
        xuli;
end.