#include <climits>
#include <vector>
#include <queue>
using namespace std;
/*
lemma: I will solve subtasks 1 and 2
proof:
*/
queue<vector<int>> q;
long long ans=0;
vector<vector<int>> visitted, exists; // both are [y][x]
vector<vector<bool>> DONE;
void bfs(int I, int x, int y, int curdist, int ox, int oy){
//cout<<"bfs called..\n";
visitted[y][x]=I;
ans %= 1000000000;
vector<int> nxt(6);
curdist++;
//cout<<I<<": visitting ["<<y<<","<<x<<"] with distance "<<curdist<<"\n";
nxt[0]=I;
nxt[3]=curdist;
nxt[4]=ox;
nxt[5]=oy;
// coords is [x,y]
// UP
if(exists[y+1][x] && visitted[y+1][x] != I){
if(exists[y+1][x] > exists[oy][ox]){
ans += curdist;
//bfs(I, x+1, y+1, curdist, oy, ox);
}
nxt[1]=x;
nxt[2]=y+1;
visitted[y+1][x]=I;
q.push(nxt);
}
// LEFT
if(exists[y][x-1] && visitted[y][x-1] != I){
if(exists[y][x-1] > exists[oy][ox]){
ans += curdist;
//bfs(I, x-1, y, curdist, oy, ox);
}
nxt[1]=x-1;
nxt[2]=y;
visitted[y][x-1]=I;
q.push(nxt);
}
// DOWN
if(exists[y-1][x] && visitted[y-1][x] != I){
//cout<<"3rd check outer alert\n";
if(exists[y-1][x] > exists[oy][ox]){
//cout<<"3rd check inner alert\n";
ans += curdist;
//bfs(I, x, y-1, curdist, oy, ox);
}
nxt[1]=x;
nxt[2]=y-1;
visitted[y-1][x]=I;
q.push(nxt);
} else{
//cout<<"\tno down.\n";
}
// RIGHT
if(exists[y][x+1] && visitted[y][x+1] != I){
if(exists[y][x+1] > exists[oy][ox]){
ans += curdist;
//bfs(I, x+1, y, curdist, oy, ox);
}
nxt[1]=x+1;
nxt[2]=y;
visitted[y][x+1]=I;
q.push(nxt);
}
//cout<<"returning..\n";
return;
}
int DistanceSum(int N, int *X, int *Y) {
DONE = vector<vector<bool>>(N+5, vector<bool>(N+5, 0));
visitted = vector<vector<int>>(N+5, vector<int>(N+5, 0));
exists = vector<vector<int>>(N+5, vector<int>(N+5, 0));
// find min X and Y values, to translate the graph to start at (1,1)
int minX=INT_MAX-1, minY=INT_MAX-1;
for(int i=0; i<N; i++){
minX = min(minX, X[i]);
minY = min(minY, Y[i]);
}
//cout<<"translating each coordinate "<<minX-1<<" to the left and "<<minY-1<<" down !\n";
for(int i=0; i<N; i++){
exists[Y[i]-minY+1][X[i]-minX+1] = i+1;
}
vector<int> cur;
for(int y=0; y<N; y++){
//cout<<"\n";
for(int x=0; x<N; x++){
//cout<<(exists[y][x] ? "#" : ".");
}
}
//cout<<"\n";
for(int i=0; i<N; i++){
bfs(i+1, X[i]-minX+1, Y[i]-minY+1, 0, X[i]-minX+1, Y[i]-minY+1);
while(!q.empty()){
cur = q.front();
q.pop();
bfs(cur[0], cur[1], cur[2], cur[3], cur[4], cur[5]);
}
}
ans %= 1000000000;
return ans;
}
