#include "books.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int n, s, ts, ans, a[1001000], cycL[1001000], cycR[1001000], L[1001000], R[1001000], dp[1001000];
bool visited[1001000];
ll cycsum;
struct Seg{
int tree[2002000], sz;
void init(int n){
sz = n;
fill(tree, tree+sz*2, 1e9);
}
void update(int p, int x){
for (tree[p+=sz]=x;p>1;p>>=1) tree[p>>1] = min(tree[p], tree[p^1]);
}
int query(int l, int r){
int ret = 1e9;
++r;
for (l+=sz, r+=sz;l<r;l>>=1, r>>=1){
if (l&1) ret = min(ret, tree[l++]);
if (r&1) ret = min(ret, tree[--r]);
}
return ret;
}
}tree1, tree2;
ll myabs(ll x){
if (x<0) return -x;
return x;
}
void dfs(int l, int r){
//printf("dfs: %d %d\n", l, r);
if (l==L[ts] && r==R[ts]) {ans += dp[L[ts]]; return;}
vector<pair<int, int>> child;
for (int i=l+1;i<r;){
if (R[i]<r){
child.emplace_back(i, R[i]);
i = R[i] + 1;
}
else i++;
}
vector<int> gl = {1}, gr = {1};
for (int i=1;i<(int)child.size();i++){
if (child[i-1].second+1==child[i].first) gl.push_back(gl.back()+1);
else gl.push_back(1);
}
for (int i=(int)child.size()-2;i>=0;i--){
if (child[i].second+1==child[i+1].first) gr.push_back(gr.back()+1);
else gr.push_back(1);
}
reverse(gr.begin(), gr.end());
for (int i=0;i<(int)child.size();i++) dp[child[i].first] = min(gl[i], gr[i]) + dp[l];
if (l==0) for (int i=0;i<(int)child.size();i++) dp[child[i].first] = (int)child.size()-1;
for (auto &[nl, nr]:child) dfs(nl, nr);
}
map<pair<int, int>, int> mp;
void naive(int s){
int ptl = s, ptr = s;
while(true){
int nl = tree1.query(ptl, ptr);
int nr = -tree2.query(ptl, ptr);
if (nl==ptl && nr==ptr) {L[s] = nl, R[s] = nr; break;}
if (mp.find(make_pair(nl, nr))!=mp.end()) {
int tmp = mp[make_pair(nl, nr)];
L[s] = L[tmp], R[s] = R[tmp];
break;
}
mp[make_pair(nl, nr)] = s;
ptl = nl, ptr = nr;
}
}
long long minimum_walk(std::vector<int> P, int S) {
int si = 0, ei = (int)P.size()-1;
for(;si<(int)P.size() && P[si]==si;si++);
for(;ei>=0 && P[ei]==ei;ei--);
if (si > ei) return 0;
n = ei-si+1;
for (int i=si;i<=ei;i++) a[i-si+1] = P[i] - si + 1;
s = S-si+1;
tree1.init(n+1);
tree2.init(n+1);
for (int i=1;i<=n;i++) if (!visited[i]){
vector<int> cyc;
for (int j=i;!visited[j];j=a[j]){
cyc.push_back(j);
visited[j] = 1;
cycR[i] = max(cycR[i], j);
cycsum += myabs(j - a[j]);
}
cycL[cycR[i]] = i;
for (auto &x:cyc){
tree1.update(x, i);
tree2.update(x, -cycR[i]);
}
}
///calc range
for (int i=1;i<=n;i++) naive(i);
/*for (int i=1;i<=n;i++) printf("(%d, %d) ", cycL[i], cycR[i]);
printf("\n");
for (int i=1;i<=n;i++) printf("(%d, %d) ", L[i], R[i]);
printf("\n");*/
if (s<=0) ts = 1, ans = 1-s;
else if (s>n) ts = n, ans = s-n;
else ts = s, ans = 0;
//printf("ok n = %d, s = %d\n", n, s);
dfs(0, n+1);
//printf("%lld + %d * 2\n", cycsum, ans);
return cycsum + ans * 2;
}
