//In the name of God
#include <bits/stdc++.h>
#include "books.h"
using namespace std;
typedef int ll;
typedef pair<ll, ll> pll;
const ll maxn = 2e6 + 100;
const ll lg = 22;
const ll mod = 1e9 + 7;
const ll inf = 1e9;
#define pb push_back
#define Mp make_pair
#define F first
#define S second
#define Sz(x) ll((x).size())
#define all(x) (x).begin(), (x).end()
#define lc (id << 1)
#define rc (lc | 1)
ll a[maxn], t, tt, c[maxn], rr[maxn], e[maxn];
ll b[maxn];
ll mn[maxn], mx[maxn], mnp[maxn], mxp[maxn];
bool vis[maxn];
vector<ll> vec, g[maxn];
vector<pll> v2;
ll seg[lg][maxn];
void bld(ll n){
for(ll i = 0; i < n; i++){
seg[0][i] = b[i];
}
for(ll j = 1; j < lg; j++){
for(ll i = 0; i + (1 << j) <= n; i++){
seg[j][i] = max(seg[j - 1][i], seg[j - 1][i + (1 << (j - 1))]);
}
}
}
ll get(ll l, ll r){
if(l < 0) l = 0;
ll f = e[r - l];
return max(seg[f][l], seg[f][r - (1 << f)]);
}
ll sz[maxn], cnt[maxn];
bool val[maxn];
ll solve(ll v, ll s){
ll x = -1;
ll ans = 0;
for(ll i = 0; i < Sz(g[v]); i++){
ll u = g[v][i];
if(mnp[u] <= s && s <= mxp[u]) x = i;
if(mnp[v] == 0){
// cout << "$ " << u << " " << mnp[u] << " " << mxp[u] << "\n";
}
ans += solve(u, s);
sz[v] += sz[u];
}
val[v] = (sz[v] == mxp[v] - mnp[v] + 1);
if(x == -1 || mnp[v] > s || s > mxp[v]) return 0;
// if(!val[g[v][x]]) cout << v << " [" << mnp[v] << ", " << mxp[v] << "] -----> " << ans << "\n";
if(!val[g[v][x]]) return ans;
ll j = 0;
ll y = inf;
ll o = mnp[g[v][x]];
for(ll i = x; i--;){
ll u = g[v][i];
if(!val[u]) continue;
j++;
if(mxp[u] + 1 != o){
y = min(y, j);
break;
}
o = mnp[u];
}
y = min(y, j + 1);
j = 0;
o = mxp[g[v][x]];
for(ll i = x + 1; i < Sz(g[v]); i++){
ll u = g[v][i];
if(!val[u]) continue;
j++;
if(mnp[u] != o + 1){
y = min(y, j);
break;
}
o = mxp[u];
}
y = min(y, j + 1);
// cout << "# " << v << " [" << mnp[v] << ", " << mxp[v] << "] -----> ";
if(mnp[v] == -1){
// cout << ans + Sz(g[v]) - 1 << "\n";
return ans + Sz(g[v]) - 1;
}
// cout << ans + y << "\n";
return ans + y;
}
long long minimum_walk(vector<int> p, int s){
for(ll i = 2; i < maxn; i++){
e[i] = e[i / 2] + 1;
}
ll n = Sz(p);
v2.reserve(n);
vec.reserve(n);
for(ll i = 0; i < n; i++){
g[i].reserve(20);
}
ll l = 0;
while(l < n && p[l] == l) l++;
ll r = n;
while(r && p[r - 1] == r - 1) r--;
if(r <= l) return 0;
l = min(l, s);
r = max(r, s + 1);
mn[0] = -1;
mx[0] = n;
t++;
long long ans = 0;
for(ll i = l; i < r; i++){
ans += abs(p[i] - i);
if(!vis[i]){
ll v = i;
mn[t] = inf;
mx[t] = -inf;
do{
cout.flush();
vis[v] = 1;
mx[t] = max(mx[t], v);
mn[t] = min(mn[t], v);
cnt[t]++;
v = p[v];
}while(v != i);
rr[mx[t]] = t;
b[mn[t]] = mx[t];
t++;
}
}
bld(n);
for(ll i = 0; i < t; i++){
v2.pb(Mp(mn[i], i));
}
fill(vis, vis + maxn, 0);
for(pll i : v2){
if(vis[i.S]) continue;
mnp[tt] = i.F;
mxp[tt] = mx[i.S];
sz[tt] = cnt[i.S];
vis[i.S] = 0;
while(true){
ll x = get(mnp[tt], mxp[tt] + 1);
if(vis[rr[x]] || x <= mxp[tt]) break;
mxp[tt] = x;
sz[tt] += cnt[rr[x]];
vis[rr[x]] = 1;
}
tt++;
}
vec.clear();
v2.clear();
ll root = -1;
for(ll i = 0; i < tt; i++){
if(mnp[i] == -1) root = i;
v2.pb(Mp(mnp[i], i));
}
sort(all(v2));
for(pll i : v2){
if(vec.empty()){
vec.pb(i.S);
continue;
}
while(mxp[vec.back()] < i.F) vec.pop_back();
g[vec.back()].pb(i.S);
vec.pb(i.S);
}
ll xx = solve(root, s);
ans += 2 * xx;
return ans;
}
