#include "books.h"
#include <bits/stdc++.h>
using namespace std;
const int inf = 1e9;
static int C[1000005];
static int L[1000000];
static int R[1000000];
void extend(int &l, int &r){
int LBound = min(L[C[l]], L[C[r]]);
int RBound = max(R[C[l]], R[C[r]]);
while(true){
if(l > LBound){
l--;
LBound = min(L[C[l]], LBound);
RBound = max(R[C[l]], RBound);
}
else if(r < RBound){
r++;
LBound = min(L[C[r]], LBound);
RBound = max(R[C[r]], RBound);
}
else break;
}
}
long long minimum_walk(vector<int> p, int S){
int n = p.size();
int leftMost = S, rightMost = S;
long long ans = 0;
int cnt = 1;
for(int i = 0;i < n;i++){
if(C[i] != 0) continue;
int x = i;
L[cnt] = i;
while(true){
C[x] = cnt;
R[cnt] = max(R[cnt], x);
ans += abs(x - p[x]); ///essential moves
x = p[x];
if(x == i) break;
}
if(i != p[i]){
leftMost = min(L[cnt], leftMost);
rightMost = max(R[cnt], rightMost);
}
cnt++;
}
int l = S, r = S;
while(true){
if(l == leftMost && r == rightMost) break;
extend(l,r);
bool hasExtension = false;
int newL = n, newR = 0;
///try to go left first
int LCost = 0;
int ll = l, rr = r; ///temporary, try first
while(true){
if(ll <= leftMost) break;
ll--; LCost += 2;
extend(ll, rr);
if(rr > r){
hasExtension = true;
break;
}
}
newL = min(ll, newL);
newR = max(rr, newR);
///then try to go right
int RCost = 0;
ll = l, rr = r; ///temporary, try first
while(true){
if(rr >= rightMost) break;
rr++; RCost += 2;
extend(ll, rr);
if(ll < l){
hasExtension = true;
break;
}
}
newL = min(ll, newL);
newR = max(rr, newR);
if(hasExtension) ans += min(LCost, RCost);
else ans += LCost + RCost;
l = newL; r = newR;
if(l == leftMost && r == rightMost) break;
}
return ans;
}
