#include "books.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 1e6 + 10;
const ll inf = 1e18;
ll used[maxn], l[maxn], r[maxn], n, dp[1030][1030];
int bef[maxn], aft[maxn];
vector < int > st[maxn];
ll distance(int l, int r, int i, int j)
{
if (i <= l && j >= r)
{
int mx = 1e9;
for (int idx : st[used[i]])
{
if (idx >= l && idx <= r)
{
mx = 0;
break;
}
mx = min(mx, abs(idx - l));
mx = min(mx, abs(idx - r));
}
return mx * 2;
}
if (i > r)
return (i - r) * 2;
if (j < l)
return (l - j) * 2;
return 0;
}
long long minimum_walk(vector<int> p, int s)
{
n = p.size();
if (n > 1000)
{
int cnt = 0;
ll mx = 0, ans = 0;
int to = 0;
for (int i = 0; i < n; i ++)
{
if (p[i] == i)
continue;
ans = ans + (ll)abs(i - p[i]);
///cout << ans << endl;
if (!used[i])
{
if (to < i)
mx = mx + i - to;
int v = p[i];
while(v != i)
{
to = max(to, v);
used[v] = 1;
v = p[v];
}
to = max(to, v);
used[v] = 1;
}
}
return ans + 2 * mx;
}
int cnt = 0;
ll ans = 0;
for (int i = 0; i < n; i ++)
{
ans = ans + abs(p[i] - i);
if (p[i] == i)
continue;
if (used[i])
continue;
cnt ++;
used[i] = cnt;
int v = p[i];
l[cnt] = i;
r[cnt] = i;
st[cnt].push_back(i);
while(v != i)
{
st[cnt].push_back(v);
used[v] = cnt;
r[cnt] = max(r[cnt], (ll)v);
v = p[v];
}
}
bef[0] = used[0];
for (int i = 1; i < n; i ++)
{
bef[i] = bef[i - 1];
if (used[i] != 0)
bef[i] = used[i];
}
aft[n - 1] = used[n - 1];
for (int i = n - 2; i >= 0; i --)
{
aft[i] = aft[i + 1];
if (used[i] != 0)
aft[i] = used[i];
}
for (int i = 0; i < n; i ++)
for (int j = 0; j < n; j ++)
dp[i][j] = inf;
dp[s][s] = 0;
///if (used[s] != 0)
/// dp[l[used[s]]][r[used[s]]] = 0;
/**cout << "-------------" << endl;
for (int i = 1; i <= cnt; i ++)
cout << l[i] << " " << r[i] << endl;
cout << "-------------" << endl;*/
for (int len = 1; len <= n; len ++)
{
for (int i = 0; i < n - len + 1; i ++)
{
int j = i + len - 1;
if (dp[i][j] == inf)
continue;
///cout << i << " " << j << " " << dp[i][j] << endl;
vector < int > idx;
/**if (i != 0 && bef[i - 1] != 0)
idx.push_back(bef[i - 1]);
if (j != n - 1 && aft[j + 1] != 0)
idx.push_back(aft[j + 1]);*/
for (int p = 1; p <= cnt; p ++)
idx.push_back(p);
for (int cur : idx)
{
int newl = min((ll)i, l[cur]);
int newr = max((ll)j, r[cur]);
if (dp[newl][newr] > dp[i][j] + distance(i, j, l[cur], r[cur]))
{
dp[newl][newr] = dp[i][j] + distance(i, j, l[cur], r[cur]);
///cout << "to " << newl << " " << newr << endl;
}
///dp[newl][newr] = min(dp[newl][newr], dp[i][j] + distance(i, j, l[cur], r[cur]));
}
}
}
int lf = 0;
int rf = n - 1;
while(lf < s && used[lf] == 0)
lf ++;
while(rf > s && used[rf] == 0)
rf --;
///cout << dp[lf][rf] << endl;
///cout << lf << " " << rf << endl;
return ans + dp[lf][rf];
}
