#include "xylophone.h"
#include <bits/stdc++.h>
using namespace std;
template<typename T>
void out(T x) { cout << x << endl; exit(0); }
#define watch(x) cout << (#x) << " is " << (x) << endl
typedef long long ll;
const ll mod = 1e9+7;
const int maxn = 1e6 + 5;
int n;
vector<int> a;
vector<int> p;
/*
//grader
int query(int s, int t) {
int lo=1e9;
int hi=-1e9;
for (int i=s; i<=t; i++) {
lo=min(lo,p[i]);
hi=max(hi,p[i]);
}
return hi-lo;
}
void answer(int i, int a) {
assert(i>=1 && i<=n);
cout<<"a["<<i<<"]: "<<a<<endl;
assert(p[i]==a);
}
//end grader
*/
int ask(int x, int y) {
if (x>y) swap(x,y);
return query(x,y);
}
void solveRange(int l, int r, int idx, bool hi=true) {
if (l>=r) return;
//cout<<"["<<l<<" "<<r<<"] : "<<idx<<" "<<hi<<endl;
if (l+1==r) {
int dx = query(l,r);
if (idx==l) {
if (hi) a[r]=a[l]-dx; else a[r]=a[l]+dx;
answer(r,a[r]);
} else {
if (hi) a[l]=a[r]-dx; else a[l]=a[r]+dx;
answer(l,a[l]);
}
} else {
int d = query(l,r);
if (idx==l) {
for (int i=r; i>=l; i--) {
int dx=query(l,i);
if (dx<d) {
if (hi) a[i+1]=a[l]-d; else a[i+1]=a[l]+d;
answer(i+1,a[i+1]);
//l..i+1..r
solveRange(l,i,l,hi);
solveRange(i+1,r,i+1,!hi);
return;
}
}
} else {
for (int i=l; i<=r; i++) {
int dx=query(i,r);
if (dx<d) {
if (hi) a[i-1]=a[r]-d; else a[i-1]=a[r]+d;
answer(i-1,a[i-1]);
//l..i-1...r
solveRange(l,i-1,i-1,!hi);
solveRange(i,r,r,hi);
return;
}
}
}
assert(0);
}
}
void solve(int N) {
n = N;
a.resize(n+1, -1);
int nIdx=-1;
for (int i=n; i>=1; i--) {
if (ask(1,i)<n-1) {
assert(i<n);
answer(i+1,n);
a[i+1]=n;
nIdx=i+1;
break;
}
}
solveRange(1,nIdx,nIdx);
solveRange(nIdx,n,nIdx);
}
vector<int> rand_perm(int n, int index=1) {
assert(n>=1);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
vector<int> a(n);
iota(a.begin(), a.end(), index);
shuffle(a.begin(), a.end(), rng);
return a;
}
// int main() {
// ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
// int siz = 20;
// p=rand_perm(siz);
// //p={5,4,2,6,1,3};
// p.insert(p.begin(), -1);
// int lo=1,hi=1;
// for (int i=1; i<=siz; i++) {
// if (p[i]>p[hi]) hi=i;
// if (p[i]<p[lo]) lo=i;
// }
// if (lo>hi) swap(p[lo],p[hi]);
// for (int i: p) cout<<i<<" ";
// cout<<endl;
// solve(siz);
// return 0;
// }
