#include <bits/stdc++.h>
#include "xylophone.h"
using namespace std;
using ll = long long;
#define MAXN (1000005)
void solve(int N) {
ll low = 1;
ll high = N + 1;
while(high - low > 1){
ll mid = (high + low) / 2;
ll diff = query(mid,N);
if(diff == N - 1){
low = mid;
}else{
high = mid;
}
}
ll posof1 = low;
ll val[N + 1]; //pos of value i
memset(val,-1,sizeof(val));
val[1] = posof1;
ll pos[N + 1]; //value of pos i
memset(pos,-1,sizeof(pos));
pos[posof1] = 1;
for(ll i = posof1 + 1;i <= N;i++){ //all index are 1-indexed
ll adjdiff = query(i - 1,i);
if(pos[i - 1] - adjdiff < 1 || val[pos[i - 1] - adjdiff] != -1){
pos[i] = pos[i - 1] + adjdiff;
val[pos[i - 1] + adjdiff] = i;
}else if(pos[i - 1] + adjdiff > N || val[pos[i - 1] + adjdiff] != -1){
pos[i] = pos[i - 1] - adjdiff;
val[pos[i - 1] - adjdiff] = i;
}else{ //I can prove this is at least 2 spaces away from val 1
ll diff = query(i - 2,i);
ll I1 = pos[i - 1] - adjdiff;
ll I2 = pos[i - 1] + adjdiff;
if(diff == abs(pos[i - 1] - pos[i - 2])){
assert(pos[i - 1] != pos[i - 2]);
if(pos[i - 1] > pos[i - 2]){
pos[i] = pos[i - 1] - adjdiff;
val[pos[i - 1] - adjdiff] = i;
}else{
pos[i] = pos[i - 1] + adjdiff;
val[pos[i - 1] + adjdiff] = i;
}
}else if(diff == max({I1,pos[i - 1],pos[i - 2]}) - min({I1,pos[i - 1],pos[i - 2]})){
assert(diff != 0);
pos[i] = I1;
val[I1] = i;
}else if(diff == max({I2,pos[i - 1],pos[i - 2]}) - min({I2,pos[i - 1],pos[i - 2]})){
assert(diff != 0);
pos[i] = I2;
val[I2] = i;
}
}
}
for(ll i = posof1 - 1;i >= 1;i--){ //all index are 1-indexed
ll adjdiff = query(i,i + 1);
if(pos[i + 1] - adjdiff < 1 || val[pos[i + 1] - adjdiff] != -1){
pos[i] = pos[i + 1] + adjdiff;
val[pos[i + 1] + adjdiff] = i;
}else if(pos[i + 1] + adjdiff > N || val[pos[i + 1] + adjdiff] != -1){
pos[i] = pos[i + 1] - adjdiff;
val[pos[i + 1] - adjdiff] = i;
}else{ //I can prove this is at least 2 spaces away from val 1
ll diff = query(i,i + 2);
ll I1 = pos[i + 1] - adjdiff;
ll I2 = pos[i + 1] + adjdiff;
if(diff == abs(pos[i + 1] - pos[i + 2])){
assert(pos[i + 1] != pos[i + 2]);
if(pos[i + 1] > pos[i + 2]){
pos[i] = pos[i + 1] - adjdiff;
val[pos[i + 1] - adjdiff] = i;
}else{
pos[i] = pos[i + 1] + adjdiff;
val[pos[i + 1] + adjdiff] = i;
}
}else if(diff == max({I1,pos[i + 1],pos[i + 2]}) - min({I1,pos[i + 1],pos[i + 2]})){
assert(diff != 0);
pos[i] = I1;
val[I1] = i;
}else if(diff == max({I2,pos[i + 1],pos[i + 2]}) - min({I2,pos[i + 1],pos[i + 2]})){
assert(diff != 0);
pos[i] = I2;
val[I2] = i;
}
}
}
for(ll i = 1;i <= N;i++){
answer(i,pos[i]);
}
}
