#include "books.h"
#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
const int maxn = 1e6 + 5;
vector<int> c(maxn, -1), L(maxn, maxn), R(maxn, -1);
void extend_for_free(int &l, int &r)
{
int tl = min({l, L[c[l]], R[c[r]]}), tr = max({r, R[c[l]], R[c[r]]});
while (tl < l || r < tr)
{
if (tl < l)
{
l--;
tl = min(tl, L[c[l]]);
tr = max(tr, R[c[l]]);
}
if (r < tr)
{
r++;
tl = min(tl, L[c[r]]);
tr = max(tr, R[c[r]]);
}
}
}
int calculate(int l, int r, int tl, int tr)
{
int ans = 0;
while (tl < l || r < tr)
{
extend_for_free(l, r);
bool left = false, right = false;
int cll = l, clr = r, crl = l, crr = r, costl = 0, costr = 0;
while (tl < cll)
{
cll--, costl += 2;
extend_for_free(cll, clr);
if (clr > r)
{
left = true;
break;
}
}
while (tr > crr)
{
crr++, costr += 2;
extend_for_free(crl, crr);
if (crl < l)
{
right = true;
break;
}
}
if (left && right) ans += min(costl, costr);
else ans += costl + costr;
l = min(cll, crl), r = max(crl, crr);
}
return ans;
}
ll minimum_walk(vector<int> p, int s)
{
int n = p.size(), num = -1, l = s, r = s;
ll ans = 0;
for (int i = 0; i < n; i++)
{
ans += abs(p[i] - i);
if (c[i] != -1) continue;
num++, L[num] = R[num] = i, c[i] = num;
int j = p[i];
while (j != i)
{
L[num] = min(L[num], j), R[num] = max(R[num], j), c[j] = num;
j = p[j];
}
if (i != p[i]) l = min(l, L[num]), r = max(r, R[num]);
}
ans += calculate(s, s, l, r);
return ans;
}
