#include "wiring.h"
#include <bits/stdc++.h>
using namespace std;
typedef vector<int> VI;
#define int long long
#define pb push_back
#define snd second
#define fst first
#define FOR(i, l, r) for(int i = (l); i < (r); i++)
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef vector<ii> vii;
const int NMAX = 2e5+10;
const int INF = 1e18+10;
int N = 0, C = 0;
vi color, pos;
vi size, dist;
vii comps;
vi le[NMAX], ri[NMAX], v[NMAX];
vi dp[NMAX];
// min segtree
struct segTree{
int size;
vi tree, lazy;
segTree(vi &arr){
size = arr.size();
tree.assign(4*size, 0);
lazy.assign(4*size, 0);
buildTree(arr, 0, size, 1);
}
void buildTree(vi &arr, int lb, int rb, int n){
if(lb+1==rb) {
tree[n] = arr[lb];
return;
}
int mb = (lb+rb)/2;
buildTree(arr, lb, mb, 2*n);
buildTree(arr, mb, rb, 2*n+1);
tree[n] = min(tree[2*n], tree[2*n+1]);
}
void recAdd(int v, int l, int r, int lb, int rb, int n){
//cout << "recAdd " << v << " " << l << " " << r << " " << lb << " " << rb << " " << n << endl;
if(l <= lb and rb <= r){
tree[n] += v;
lazy[n] += v;
return;
}
int mb = (lb+rb)/2;
if(lazy[n]){
recAdd(lazy[n], lb, rb, lb, mb, 2*n);
recAdd(lazy[n], lb, rb, mb, rb, 2*n+1);
lazy[n] = 0;
}
if(l < mb) recAdd(v, l, r, lb, mb, 2*n);
if(r > mb) recAdd(v, l, r, mb, rb, 2*n+1);
tree[n] = min(tree[2*n], tree[2*n+1]);
}
int zero(int rb, int n=1){
if(rb == 1) return tree[n];
int mb = rb/2;
if(lazy[n]){
recAdd(lazy[n], 0, rb, 0, mb, 2*n);
recAdd(lazy[n], 0, rb, mb, rb, 2*n+1);
lazy[n] = 0;
}
return zero(mb, 2*n);
}
int zero(){
return zero(size);
}
void add(int v, int l){
recAdd(v, l, size, 0, size, 1);
}
int mq(){
return tree[1];
}
};
long long min_total_length(VI r, VI b) {
N = r.size() + b.size();
int i = 0, j = 0;
r.pb(1e9+10); b.pb(1e9+10);
while(i + j < N){
//cout << i << " " << j << endl;
if(r[i] < b[j]) {
pos.pb(r[i++]);
color.pb(0);
} else {
pos.pb(b[j++]);
color.pb(1);
}
}
int start = 0;
//cout << "Built pos" << endl;
FOR(i, 1, N){
if(color[i-1] != color[i]){
comps.pb({start, i-1});
size.pb(i-start);
start = i;
}
}
comps.pb({start, N-1});
size.pb(N-start);
C = comps.size();
//cout << "Built comps" << endl;
FOR(i, 0, C){
//cout << i << endl;
int s = size[i];
le[i].assign(s+1, 0); ri[i].assign(s+1, 0);
// leftmost, rightmost
int l = pos[comps[i].fst], r = pos[comps[i].snd];
FOR(j, 1, s+1) le[i][j] = le[i][j-1] + pos[comps[i].fst + j-1] - l;
for(int j = s-1; j >= 0; j--) ri[i][j] = ri[i][j+1] + r - pos[comps[i].fst + j];
}
//dp[i][k] => min wire needed to connect comp i onwards, given that k wires are coming in from the left
dist.assign(C, 0);
dist[0] = INF;
FOR(i, 1, C) dist[i] = pos[comps[i].fst] - pos[comps[i-1].snd];
FOR(i, 0, C) FOR(j, 0, le[i].size()) v[i].pb(le[i][j] + ri[i][j]);
dp[C].pb(0);
dp[C].pb(INF);
for(int i = C-1; i >= 0; i--){
//cout << "i = " << i << endl;
// dp[C]
vi arr(size[i]+1, 0);
dp[i].assign(size[i]+1, INF);
FOR(j, 0, size[i]+1) {
arr[j] = v[i][j] + dp[i+1][ min(size[i] - j, (int) dp[i+1].size() -1 ) ];
if(i != C and size[i]-j > (int)dp[i+1].size()-1){
arr[j] += dist[i+1] * (size[i]-j - (int) dp[i+1].size()+1);
}
}
//cout << "Made array" << endl;
segTree t(arr);
//cout << "Built tree" << endl;
int extra = size[i] * dist[i];
dp[i][size[i]] = t.mq() + extra;
for(int k = size[i]-1; k >= 0; k--){
//cout << "k = " <<k<<endl;
t.add(dist[i], k+1);
//cout << "added" << endl;
extra -= dist[i];
dp[i][k] = t.mq() + extra;
if(i == 0) dp[i][k] = t.zero();
}
}
/*
cout << "pos: \t\t";
for(int k : pos) cout << k << " ";
cout << endl;
cout << "color: \t\t";
for(int k : color) cout << k << " ";
cout << endl;
cout << "comps: \t\t";
for(ii k : comps) cout << k.fst << " " << k.snd << "\t";
cout << endl;
cout << "dist: \t\t";
for(int k : dist) cout << k << " ";
cout << endl;
cout << "left: \n";
FOR(i, 0, C) {
for(int k : le[i]) cout << k << " ";
cout << endl;
}
cout << "right: \n";
FOR(i, 0, C) {
for(int k : ri[i]) cout << k << " ";
cout << endl;
}
cout << "v: \n";
FOR(i, 0, C) {
for(int k : v[i]) cout << k << " ";
cout << endl;
}
segTree t(pos);
t.add(-9, 5);
cout << t.mq() << endl;
cout << "dp: \n";
FOR(i, 0, C+1) {
for(int k : dp[i]) cout << k << " ";
cout << endl;
}
*/
return dp[0][0];
}
/*
4 5
1 2 3 7
0 4 5 9 10
5 3
1 3 9 102 103
5 125 130
*/
