#include "books.h"
#include <bits/stdc++.h>
using namespace std;
typedef vector<int> vi;
typedef long long ll;
#define sz(x) (int)(x).size()
#define pb push_back
#define bk back()
const int MOD = 1e9+7;
const int mx = 1000005;
vi p;
int s;
int cycL[mx]; //leftmost of a cycle
int cycR[mx]; //rightmost of a cycle
void popLRSingles(){
int L = 0;
for(int i = 0; i < s; i++){
if(p[i] == i){
L = i+1;
}
else{
break;
}
}
vi newp;
for(int i = L; i < sz(p); i++){
newp.pb(p[i]);
}
p = newp;
s = s-L;
while(true){
if(sz(p)-1 == s) break;
if(p[sz(p)-1] == sz(p)-1){
p.pop_back();
}
else{
break;
}
}
}
int curL, curR;
vi Lfrees, Rfrees;
void getFrees(){
while(true){
bool updated = false;
while(sz(Lfrees)){
int node = Lfrees.bk;
if(node < curL) break;
updated = true;
Lfrees.pop_back();
curL = min(curL, cycL[node]);
curR = max(curR, cycR[node]);
}
while(sz(Rfrees)){
int node = Rfrees.bk;
if(node > curR) break;
updated = true;
Rfrees.pop_back();
curL = min(curL, cycL[node]);
curR = max(curR, cycR[node]);
}
if(!updated) break;
}
}
long long minimum_walk(vi _p, int _s) {
p = _p;
s = _s;
popLRSingles();
int n = sz(p);
for(int i = 0; i < n; i++){
cycL[i] = MOD;
cycR[i] = -1;
}
for(int i = 0; i < n; i++){
if(cycR[i] == -1){
int curnode = i;
vi cycle_nodes;
while(true){
cycle_nodes.pb(curnode);
curnode = p[curnode];
if(curnode == i) break;
}
for(auto u: cycle_nodes){
cycL[i] = min(cycL[i], u);
cycR[i] = max(cycR[i], u);
}
for(auto u: cycle_nodes){
cycL[u] = cycL[i];
cycR[u] = cycR[i];
}
}
}
ll ans = 0;
for(int i = 0; i < n; i++){
ans+=abs(p[i]-i);
}
curL = s;
curR = s;
for(int i = 0; i <= s; i++){
Lfrees.pb(i);
}
for(int i = n-1; i >= s; i--){
Rfrees.pb(i);
}
getFrees();
while(curL > 0 || curR < n-1){
int prev_curL = curL;
int prev_curR = curR;
ll L_cost = 0;
ll R_cost = 0;
bool non_boost = false;
for(int i = curL-1; i >= 0; i--){
if(i+1 == curL){
L_cost+=2;
curL--;
}
curL = min(curL, cycL[i]);
if(cycR[i] > prev_curR){
//found non boost
non_boost = true;
break;
}
}
for(int i = curR+1; i < n; i++){
if(i-1 == curR){
R_cost+=2;
curR++;
}
curR = max(curR, cycR[i]);
if(cycL[i] < prev_curL){
non_boost = true;
break;
}
}
if(!non_boost){
ans+=L_cost+R_cost;
}
else{
ans+=min(L_cost, R_cost);
}
getFrees();
}
return ans;
}
