#include <bits/stdc++.h>
struct Seg {
int size;
std::vector <int> min;
std::vector <int> max;
Seg(int s) {
size = 1;
while (size < s) {
size <<= 1;
}
max.resize(size << 1, -1);
min.resize(size << 1, 1 << 30);
}
inline void build(const std::vector <int>& mn, const std::vector <int>& mx) {
build(mn, mx, 0, 0, size);
}
void build(const std::vector <int>& mn, const std::vector <int>& mx, int now, int l, int r) {
if (!(r - l - 1)) {
if (l < (int) mn.size()) {
min[now] = mn[l];
}
if (l < (int) mx.size()) {
max[now] = mx[l];
}
return;
}
int mid = (l + r) >> 1;
build(mn, mx, now * 2 + 1, l, mid);
build(mn, mx, now * 2 + 2, mid, r);
max[now] = std::max(max[now * 2 + 1], max[now * 2 + 2]);
min[now] = std::min(min[now * 2 + 1], min[now * 2 + 2]);
}
inline int query_min(int l, int r) {
return query_min(l, r, 0, 0, size);
}
int query_min(int tl, int tr, int now, int l, int r) {
if (l >= tr || r <= tl) {
return 1 << 30;
}
if (l >= tl && r <= tr) {
return min[now];
}
int mid = (l + r) >> 1;
return std::min(query_min(tl, tr, now * 2 + 1, l, mid), query_min(tl, tr, now * 2 + 2, mid, r));
}
inline int query_max(int l, int r) {
return query_max(l, r, 0, 0, size);
}
int query_max(int tl, int tr, int now, int l, int r) {
if (l >= tr || r <= tl) {
return -1;
}
if (l >= tl && r <= tr) {
return max[now];
}
int mid = (l + r) >> 1;
return std::max(query_max(tl, tr, now * 2 + 1, l, mid), query_max(tl, tr, now * 2 + 2, mid, r));
}
};
struct Cycle {
std::vector <int> c;
int l, r;
};
long long minimum_walk(std::vector <int> p, int s) {
int n = p.size();
while (s < (int) p.size() - 1 && p[n - 1] == n - 1) {
p.pop_back();
n--;
}
int begrem = 0;
while (begrem < s && p[begrem] == begrem) {
begrem++;
}
p.erase(p.begin(), p.begin() + begrem);
n = p.size();
s -= begrem;
for (int& x : p) {
x -= begrem;
}
if (!n) {
return 0;
}
std::vector <bool> vis(n, false);
std::vector <Cycle> cyc;
std::vector <int> part(n, -1);
long long ans = 0;
for (int i = 0; i < n; i++) {
if (vis[i]) {
continue;
}
vis[i] = true;
int part_now = cyc.size();
cyc.resize(cyc.size() + 1);
cyc.back().c = { i };
cyc.back().l = cyc.back().r = i;
ans += abs(i - p[i]);
int v = p[i];
part[i] = part_now;
while (v != i) {
vis[v] = true;
cyc.back().c.push_back(v);
cyc.back().l = std::min(cyc.back().l, v);
cyc.back().r = std::max(cyc.back().r, v);
part[v] = part_now;
ans += abs(v - p[v]);
v = p[v];
};
}
Seg seg(n);
std::vector <int> mn(n), mx(n);
for (int i = 0; i < n; i++) {
mn[i] = cyc[part[i]].l;
mx[i] = cyc[part[i]].r;
}
seg.build(mn, mx);
int cmps = 0;
int l = 0, r = 0;
int last;
int ll = -1, rr = -1;
while (r < n) {
while ((last = seg.query_max(l, r + 1)) > r) {
r = last;
}
if (l <= s && r >= s) {
ll = l;
rr = r;
}
l = ++r;
cmps++;
}
l = s, r = s;
int last_l, last_r;
cmps--;
while (l >= ll) {
while (true) {
last_l = seg.query_min(l, r + 1);
last_r = seg.query_max(l, r + 1);
if (last_l >= l && last_r <= r) {
break;
}
l = last_l;
r = last_r;
}
l--;
r++;
cmps++;
}
return ans + (cmps - 1) * 2;
}
