/*
ID: varunra2
LANG: C++
TASK: rail
*/
#include<bits/stdc++.h>
#include "rail.h"
using namespace std;
#ifdef DEBUG
#include "lib/debug.h"
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define debug_arr(...) \
cerr << "[" << #__VA_ARGS__ << "]:", debug_arr(__VA_ARGS__)
#pragma GCC diagnostic ignored "-Wsign-compare"
//#pragma GCC diagnostic ignored "-Wunused-parameter"
//#pragma GCC diagnostic ignored "-Wunused-variable"
#else
#define debug(...) 42
#endif
#define EPS 1e-9
#define IN(A, B, C) assert(B <= A && A <= C)
#define INF (int)1e9
#define MEM(a, b) memset(a, (b), sizeof(a))
#define MOD 1000000007
#define MP make_pair
#define PB push_back
#define all(cont) cont.begin(), cont.end()
#define rall(cont) cont.end(), cont.begin()
#define x first
#define y second
const double PI = acos(-1.0);
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef map<int, int> MPII;
typedef multiset<int> MSETI;
typedef set<int> SETI;
typedef set<string> SETS;
typedef vector<int> VI;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<string> VS;
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define trav(a, x) for(auto& a : x)
#define sz(x) (int)(x).size()
typedef pair<int, int> pii;
typedef vector<int> vi;
#pragma GCC diagnostic ignored "-Wsign-compare"
// util functions
// int getDistance(int a, int b) {
// return 42069; // hehe funi numbers
// }
void findLocation(int n, int frst, int location[], int stype[]) {
VII vals(n, MP(0, 0));
for(int i = 1; i < n; i++) {
vals[i] = MP(getDistance(0, i), i);
}
sort(vals.begin() + 1, vals.end());
int nxt = vals[1].y;
location[0] = frst;
stype[0] = 1;
stype[nxt] = 2;
location[nxt] = frst + vals[1].x;
SETI a, b;
int l = 0, r = nxt;
a.insert(location[l]); b.insert(location[r]);
for(int cnt = 2; cnt < n; cnt++) {
auto x = vals[cnt];
int ind, dist;
tie(dist, ind) = x;
int nxtdist = getDistance(nxt, ind);
if(nxtdist + vals[1].x == dist and location[nxt] - nxtdist < frst) {
int dist1 = getDistance(l, ind);
int pos = dist1 + location[l];
auto it = a.lower_bound(pos);
it--;
int val = *it;
if(location[nxt] + pos == nxtdist + 2 * val) {
location[ind] = pos;
stype[ind] = 2;
}
else {
location[ind] = location[nxt] - nxtdist;
stype[ind] = 1;
a.insert(location[ind]);
l = ind;
}
}
else {
int dist1 = getDistance(r, ind);
int pos = location[r] - dist1;
auto it = b.upper_bound(pos);
int val = *it;
if(dist + pos + frst == 2 * val) {
location[ind] = pos;
stype[ind] = 1;
}
else {
location[ind] = frst + dist;
stype[ind] = 2;
b.insert(location[ind]);
r = ind;
}
}
}
}
// int main() {
// #ifndef ONLINE_JUDGE
// freopen("rail.in", "r", stdin);
// freopen("rail.out", "w", stdout);
// #endif
// cin.sync_with_stdio(0); cin.tie(0);
// return 0;
// }
