#include "books.h"
#include <bits/stdc++.h>
using namespace std;
const int maxN = 1e6 + 20;
int cycleL[maxN];
int cycleR[maxN];
void extend(int &curL, int &curR) {
int nxtL = min(curL, cycleL[curL]);
int nxtR = max(curR, cycleR[curR]);
while (curL > nxtL || curR < nxtR) {
if (curL > nxtL) {
curL--;
nxtL = min(nxtL, cycleL[curL]);
}
else {
curR++;
nxtR = max(nxtR, cycleR[curR]);
}
}
}
long long minimum_walk(vector<int> A, int start) {
int N = A.size();
for (int i = 0; i < N; i++) {
cycleL[i] = -1;
cycleR[i] = -1;
}
int curL = start;
int curR = start;
int endL = start;
int endR = start;
long long res = 0;
for (int i = 0; i < N; i++) {
if (i != A[i]) {
endL = min(endL, i);
endR = max(endR, i);
}
res += abs(A[i] - i);
if (cycleL[i] == -1) {
int L = i;
int R = i;
int cur = i;
do {
L = min(L, cur);
R = max(R, cur);
cur = A[cur];
}
while (cur != i);
cur = i;
do {
cycleL[cur] = L;
cycleR[cur] = R;
cur = A[cur];
}
while (cur != i);
}
}
while (curL > endL || curR < endR) {
extend(curL, curR);
int costL = 0;
int nxtLL = curL;
int nxtLR = curR;
while (nxtLL > endL && nxtLR == curR) {
nxtLL--;
costL += 2;
extend(nxtLL, nxtLR);
}
int costR = 0;
int nxtRL = curL;
int nxtRR = curR;
while (nxtRR < endR && nxtRL == curL) {
nxtRR++;
costR += 2;
extend(nxtRL, nxtRR);
}
if (nxtLR == curR && nxtRL == curL) {
res += costL + costR;
}
else {
res += min(costL, costR);
}
curL = min(nxtLL, nxtRL);
curR = max(nxtLR, nxtRR);
}
return res;
}
