#include "books.h"
#include <bits/stdc++.h>
using ll = long long;
using std::pair;
using std::vector;
ll minimum_walk(vector<int> P, int s) {
{
int l = 0, r = (int)P.size() - 1;
while (l < s and P[l] == l) {
l += 1;
}
while (r > s and P[r] == r) {
r -= 1;
}
P.erase(P.begin() + r + 1, P.end());
P.erase(P.begin(), P.begin() + l);
s -= l;
}
const int N = (int)P.size();
vector<char> seen(N);
vector<int> left(N), right(N);
ll ans = 0;
for (int i = 0; i < N; ++i) {
ans += std::abs(P[i] - i);
if (seen[i]) {
continue;
}
vector<int> cycle;
for (int j = i; !seen[j]; j = P[j]) {
seen[j] = true;
cycle.push_back(j);
}
const int l = *std::min_element(cycle.begin(), cycle.end());
const int r = *std::max_element(cycle.begin(), cycle.end());
for (const int j : cycle) {
left[j] = l;
right[j] = r;
}
}
const auto extend = [&](int& l, int& r) {
int a = left[l], b = right[r];
while (a < l or r < b) {
if (a < l) {
l -= 1;
a = std::min(a, left[l]);
b = std::max(b, right[l]);
} else {
r += 1;
a = std::min(a, left[r]);
b = std::max(b, right[r]);
}
}
};
int l = s, r = s;
while (true) {
extend(l, r);
int xl = l, xr = r, xc = 0;
while (0 < xl and xr <= r) {
xl -= 1;
xc += 2;
extend(xl, xr);
}
int yl = l, yr = r, yc = 0;
while (l <= yl and yr < N - 1) {
yr += 1;
yc += 2;
extend(yl, yr);
}
if (xr <= r) {
ans += xc + yc;
break;
}
ans += std::min(xc, yc);
l = std::min(xl, yl);
r = std::max(xr, yr);
}
return ans;
}
