#include "books.h"
#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
int crit_l, crit_r;
int cmp[1000000], cmp_l[1000000], cmp_r[1000000];
map<pair<int, int>, ll> dp;
void extend(int &l, int &r) {
int ext_l = min(cmp_l[cmp[l]], cmp_l[cmp[r]]);
int ext_r = max(cmp_r[cmp[l]], cmp_r[cmp[r]]);
while (l != ext_l || r != ext_r) {
if (l != ext_l) {
l--;
ext_l = min(ext_l, cmp_l[cmp[l]]);
ext_r = max(ext_r, cmp_r[cmp[l]]);
} else {
r++;
ext_l = min(ext_l, cmp_l[cmp[r]]);
ext_r = max(ext_r, cmp_r[cmp[r]]);
}
}
}
ll compute(int l, int r) {
extend(l, r);
if (dp.count({l, r})) return dp[{l, r}];
if (l == crit_l) return dp[{l, r}] = compute(l, r + 1) + 2;
if (r == crit_r) return dp[{l, r}] = compute(l - 1, r) + 2;
ll to_l = 2, to_r = 2;
int nl, nr, tl, tr;
nl = l - 1, nr = r, tl = l, tr = r + 1;
extend(nl, nr), extend(tl, tr);
while (nl != crit_l && nr < tr) {
to_l += 2;
nl--;
extend(nl, nr);
}
if (nr < tr) return dp[{l, r}] = to_l + compute(nl, nr);
nl = l, nr = r + 1, tl = l - 1, tr = r;
extend(nl, nr), extend(tl, tr);
while (nr != crit_r && nl > tl) {
to_r += 2;
nr++;
extend(nl, nr);
}
return dp[{l, r}] = min(to_l, to_r) + compute(nl, nr);
}
ll minimum_walk(vector<int> p, int s) {
int n = p.size(), cmp_cnt = 0;
fill(cmp, cmp + n, -1);
crit_l = s, crit_r = s;
ll intra = 0;
for (int i = 0; i < n; i++) {
intra += abs(p[i] - i);
if (cmp[i] == -1) {
int curr = i;
cmp_l[cmp_cnt] = cmp_r[cmp_cnt] = i;
do {
cmp[curr] = cmp_cnt;
cmp_r[cmp_cnt] = max(cmp_r[cmp_cnt], curr);
curr = p[curr];
} while (curr != i);
if (i != p[i]) {
crit_l = min(crit_l, cmp_l[cmp_cnt]);
crit_r = max(crit_r, cmp_r[cmp_cnt]);
}
cmp_cnt++;
}
}
dp[{crit_l, crit_r}] = 0;
return intra + compute(s, s);
}
