#include <bits/stdc++.h>
#include <unordered_map>
using namespace std;
#define rep(i,a,b) for (int i = (a); i < (b); i++)
#define pb push_back
typedef long long ll;
typedef pair<int, int> pii;
#include "books.h"
long long minimum_walk(std::vector<int> p, int s)
{
int cycles = 0;
vector<int> cycle(p.size(), -1);
vector<pii> lohi;
ll base = 0;
rep(i,0,p.size())
{
if (p[i] == i) cycle[i] = -1;
else if (cycle[i] == -1)
{
cycle[i] = cycles;
base += abs(i - p[i]);
int at = p[i], low = i, high = i;
while (at != i)
{
if (at < low) low = at;
if (at > high) high = at;
base += abs(at - p[at]);
cycle[at] = cycles;
at = p[at];
}
lohi.pb(make_pair(low, high));
cycles++;
}
}
ll add = 0;
if (s == 0)
{
int low = 0, high = 0; // inc
//int ind = 0;
rep(i,0,cycle.size())
{
if (cycle[i] == -1) continue;
if (i > high) add += (i - high) * 2;
high = max(high, lohi[cycle[i]].second);
}
}
else
{
vector<int> closest(cycle.size(), -1);
if (cycle[0] == -1) closest[0] = -1;
else closest[0] = 0;
rep(i,1,s)
{
if (cycle[i] == -1) closest[i] = closest[i - 1];
else closest[i] = i;
}
if (cycle[cycle.size() - 1] == -1) closest[cycle.size() - 1] = -1;
else closest[cycle.size() - 1] = cycle.size() - 1;
for (int i = cycle.size() - 2; i > s; i--)
{
if (cycle[i] == -1) closest[i] = closest[i + 1];
else closest[i] = i;
}
// edges
int low = s, high = s;
if (cycle[s] != -1)
{
low = lohi[cycle[s]].first;
high = lohi[cycle[s]].second;
}
//
map<pii, ll> dp; // ??
priority_queue<array<ll, 3>> pq;
pq.push({-0, low, high});
dp[make_pair(low, high)] = -1;
while (!pq.empty())
{
auto x = pq.top();
pq.pop();
ll steps = x[0];
steps = -steps;
low = x[1];
high = x[2];
//
int go = -1;
if (low > 0 && high < cycle.size() - 1)
{
if (closest[low - 1] == -1)
{
low = 0;
// continue;
}
if (closest[high + 1] == -1)
{
high = cycle.size() - 1;
// continue;
}
}
if (low > 0 && high < cycle.size() - 1)
{
int low1 = low, high1 = high, steps1 = steps;
go = closest[low - 1];
steps1 += (low - closest[low - 1]) * 2;
low1 = min(low, lohi[cycle[go]].first);
high1 = max(high, lohi[cycle[go]].second);
if (dp[make_pair(low1, high1)] == 0)
{
if (low1 == 0 && high1 == cycle.size() - 1)
{
add = steps1;
break;
}
dp[make_pair(low1, high1)] = steps1;
pq.push({-steps1, low1, high1});
}
//
low1 = low, high1 = high, steps1 = steps;
go = closest[high + 1];
steps1 += (closest[high + 1] - high) * 2;
low1 = min(low, lohi[cycle[go]].first);
high1 = max(high, lohi[cycle[go]].second);
if (dp[make_pair(low1, high1)] == 0 || steps1 < dp[make_pair(low1, high1)]) // dp[make_pair(low1, high1)] == 0
{
if (low1 == 0 && high1 == cycle.size() - 1)
{
add = steps1;
break;
}
dp[make_pair(low1, high1)] = steps1;
pq.push({-steps1, low1, high1});
}
continue;
}
else if (high < cycle.size() - 1)
{
if (closest[high + 1] == -1)
{
add = steps;
break;
}
go = closest[high + 1];
steps += (closest[high + 1] - high) * 2;
}
else if (low > 0)
{
if (closest[low - 1] == -1)
{
add = steps;
break;
}
go = closest[low - 1];
steps += (low - closest[low - 1]) * 2;
}
if (go == -1)
{
add = steps;
break;
}
low = min(low, lohi[cycle[go]].first);
high = max(high, lohi[cycle[go]].second);
//
if (dp[make_pair(low, high)] != 0) continue; // ??
dp[make_pair(low, high)] = steps;
if (low == 0 && high == cycle.size() - 1)
{
add = steps;
break;
}
pq.push({-steps, low, high});
}
//
}
ll ans = base + add;
return ans;
}
