#include "xylophone.h"
#include <bits/stdc++.h>
#define int long long
using namespace std;
static int A[5001];
static bool isLess[5001][5001];
static int queries[5001][5001];
// On a |a[i+1] - a[i]|, |a[i+2] - a[i+1]|, max(...)
// a[i] < a[i+2] < a[i+1] : z = x
// a[i+1] < a[i+2] < a[i] : z = x
//
// a[i+1] < a[i] < a[i+2] : z = y
// a[i+2] < a[i] < a[i+1] : z = y
// a[i+2] < a[i+1] < a[i] : z > x,y
// a[i] < a[i+1] < a[i+2] : z > x,y
void solve(signed N)
{
isLess[1][2] = true;
for (int i(1); i < N; ++i)
queries[i][i+1] = query(i,i+1);
for (int i(1); i < N-1; ++i)
queries[i][i+2] = query(i, i+2);
for (int i(1); i+2 <= N; ++i)
{
int x(queries[i][i+1]), y(queries[i+1][i+2]), z(queries[i][i+2]);
if (x == z)
{
if (isLess[i][i+1])
isLess[i][i+2] = true, isLess[i+2][i+1] = true;
else
isLess[i+2][i] = true, isLess[i+1][i+2] = true;
}
else if (z == y)
{
if (isLess[i][i+1])
isLess[i+2][i] = isLess[i+2][i+1] = true;
else
isLess[i+1][i+2] = isLess[i][i+2] = true;
}
else
{
if (isLess[i][i+1])
isLess[i][i+2] = isLess[i+1][i+2] = true;
else
isLess[i+2][i+1] = isLess[i+2][i] = true;
}
}
for (int flip(0); flip < 2; ++flip)
{
vector<bool> seen(N+1, false);
A[1] = 0;
for (int i(2); i <= N; ++i)
{
if (isLess[i-1][i] ^ flip)
A[i] = A[i-1] + queries[i-1][i];
else
A[i] = A[i-1] - queries[i-1][i];
}
int posMin(1);
for (int i(2); i <= N; ++i)
if (A[i] < A[posMin])
posMin = i;
int delta = A[posMin] - 1;
for (int i(1); i <= N; ++i)
A[i] -= delta;
bool ok(true);
for (int i(1); ok and i <= N; ++i)
{
if (A[i] < 1 or A[i] > N or seen[A[i]] or (i == posMin and seen[N]))
ok = false;
else
seen[A[i]] = true;
}
if (ok)
{
for (int i(1); i <= N; ++i)
answer(i, A[i]);
return ;
}
}
assert(false);
}
