#include "books.h"
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef pair<ll, ll> pii;
typedef vector<pii> vpii;
typedef vector<vpii> vvpii;
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
const ll INF = 1LL << 60;
int N;
ll safecost;
vi vis, P;
void cycle(int i, int &mini, int &maxi, int cycleCnt)
{
if (vis[i] != -1)
return;
mini = min(mini, i);
maxi = max(maxi, i);
vis[i] = cycleCnt;
safecost += (ll)abs(P[i] - i);
cycle(P[i], mini, maxi, cycleCnt);
}
long long minimum_walk(std::vector<int> p, int s)
{
N = sz(p);
P.resize(N);
for (int i = 0; i < N; ++i)
P[i] = p[i];
vis.assign(N, -1);
ll L = INF, R = -1;
safecost = 0;
vpii borders;
for (int i = 0, mini, maxi; i < N; ++i)
{
if (P[i] != i)
L = min(L, (ll)i), R = max(R, (ll)i);
if (vis[i] == -1 && P[i] != i)
{
mini = maxi = i;
cycle(i, mini, maxi, sz(borders));
borders.push_back({mini, maxi});
}
}
if (borders.empty())
return 0;
if (s <= L || s >= R)
{
if (s >= R)
{
s = N - s;
for (int i = 0, l, r; i < sz(borders); ++i)
{
tie(l, r) = borders[i];
borders[i] = {N - r, N - l};
}
}
sort(all(borders));
ll pos = s;
for (pii b : borders)
{
safecost += 2 * max(0LL, b.first - pos);
pos = max(pos, b.second);
}
return safecost;
}
vi maxL(N, s), maxR(N, s), cost(N, 0);
if (vis[s] != -1)
tie(maxL[s], maxR[s]) = borders[vis[s]];
for (int i = s + 1; i < N; ++i)
{
maxL[i] = maxL[i - 1], maxR[i] = maxR[i - 1], cost[i] = cost[i - 1];
if (maxR[i] < i)
cost[i] += 2, maxR[i] = i;
if (vis[i] != -1)
maxL[i] = min(maxL[i], borders[vis[i]].first),
maxR[i] = max(maxR[i], borders[vis[i]].second);
}
for (int i = s - 1; i >= 0; --i)
{
maxL[i] = maxL[i + 1], maxR[i] = maxR[i + 1], cost[i] = cost[i + 1];
if (maxL[i] > i)
cost[i] += 2, maxL[i] = i;
if (vis[i] != -1)
maxL[i] = min(maxL[i], borders[vis[i]].first),
maxR[i] = max(maxR[i], borders[vis[i]].second);
}
ll mincost = INF;
int l = s, r = N - 1;
while (l >= 0 && r >= 0)
{
int virtualL = min(maxL[l], maxL[maxL[r]]);
if (max(maxR[l], maxR[r]) < R || virtualL > L)
--l;
else
{
ll tmp = safecost + cost[r];
if (l < maxL[r])
tmp += cost[l] - cost[maxL[r]];
mincost = min(mincost, tmp);
--r;
}
}
return mincost;
}
