#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#include "xylophone.h"
void solve(int n)
{
vector<vector<int>> a(n + 1, vector<int>(n + 1));
vector<set<pair<int, int>>> s(n + 1);
for (int i = 1; i < n; ++i)
{
a[i][i + 1] = query(i, i + 1);
s[a[i][i + 1]].insert({i, i + 1});
}
for (int i = 1; i < n - 1; ++i)
{
int v = query(i, i + 2);
if (v == a[i][i + 1] + a[i + 1][i + 2])
{
a[i][i + 2] = v;
s[v].insert({i, i + 2});
}
else
{
if (v == a[i][i + 1])
{
a[i][i + 2] = v - a[i + 1][i + 2];
s[a[i][i + 2]].insert({i, i + 2});
}
else
{
a[i][i + 2] = v - a[i][i + 1];
s[a[i][i + 2]].insert({i, i + 2});
}
}
}
for (int i = 3; i < n; ++i)
{
int sum(0);
for (int j = 1; j < i - 1; ++j)
sum += a[j][j + 1];
for (int j = 1; j <= n - i; ++j)
{
sum -= a[j - 1][j];
sum += a[j + i - 1][j + i];
int v = query(j, i + j);
if (v == sum)
{
a[j][i + j] = v;
s[v].insert({j, i + j});
}
else
{
auto t = s[v].lower_bound({j, 0});
if (t->first == j)
{
a[j][i + j] = v - a[t->second][j + i];
s[a[j][i + j]].insert({j, i + j});
}
else if (t->second == j + i)
{
a[j][i + j] = v - a[j][t->first];
s[a[j][j + i]].insert({j, j + i});
}
else
{
a[j][i + j] = v - min(a[j][t->first] + a[t->second][j + i], a[j][t->second] + a[t->first][j + i]);
s[a[j][j + i]].insert({j, j + i});
}
}
}
}
int pos(-1);
for (int i = 1; i <= n; ++i)
{
for (int j = i + 1; j <= n; ++j)
if (a[i][j] == n - 1)
{
pos = i;
break;
}
if (pos != -1)
break;
}
for (int i = 1; i <= n; ++i)
{
if (i == pos)
answer(i, 1);
else
answer(i, 1 + (i < pos ? a[i][pos] : a[pos][i]));
}
}
