Problem:
Score: 600 points

Problem Statement

AtCoder's head office consists of N rooms numbered 1 to N. For any two rooms, there is a direct passage connecting these rooms.

For security reasons, Takahashi the president asked you to set a level for every passage, which is a positive integer and must satisfy the following condition:

For each room i\ (1 \leq i \leq N), if we leave Room i, pass through some passages whose levels are all equal and get back to Room i, the number of times we pass through a passage is always even.

Your task is to set levels to the passages so that the highest level of a passage is minimized.

Constraints

N is an integer between 2 and 500 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print one way to set levels to the passages so that the objective is achieved, as follows:

a_{1,2} a_{1,3} ... a_{1,N}
a_{2,3} ... a_{2,N}
.
.
.
a_{N-1,N}

Here a_{i,j} is the level of the passage connecting Room i and Room j.

If there are multiple solutions, any of them will be accepted.

Sample Input 1

3

Sample Output 1

1 2
1

The following image describes this output:

For example, if we leave Room 2, traverse the path 2 \to 3 \to 2 \to 3 \to 2 \to 1 \to 2 while only passing passages of level 1 and get back to Room 2, we pass through a passage six times.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#pragma GCC optimize("O3", "unroll-loops")
//#pragma GCC target("avx2")
 
#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <bitset>
#include <sstream>
#include <deque>
#include <queue>
#include <random>
#include <cassert>
 
using namespace std;
 
#define FAST ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define FIXED cout << fixed << setprecision(12)
#define RANDOM srand(94385)
#define ll long long
#define ld long double
#define pii pair<int, int>
#define pll pair<ll, ll>
#define graph vector<vector<int>>
#define pb push_back
#define pf push_front
#define popb pop_back
#define popf pop_front
#define f first
#define s second
#define hashmap unordered_map
#define hashset unordered_set
#define eps 1e-9
#define mod 1000000007
#define inf 3000000000000000007ll
#define sz(a) signed(a.size())
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define shuffle(a) \
    for (int i = 0; i < sz(a); ++i) \
        swap(a[i], a[rand() % sz(a)]);
 
template<class T, class U> inline void checkmin(T &x, U y) { if (y < x) x = y; }
template<class T, class U> inline void checkmax(T &x, U y) { if (y > x) x = y; }
template<class T, class U> inline bool ifmax(T &x, U y) { if (y > x) return x = y, true; return false; }
template<class T, class U> inline bool ifmin(T &x, U y) { if (y < x) return x = y, true; return false; }
template<class T> inline void sort(T &a) { sort(all(a)); }
template<class T> inline void rsort(T &a) { sort(rall(a)); }
template<class T> inline void reverse(T &a) { reverse(all(a)); }
template<class T, class U> inline istream& operator>>(istream& str, pair<T, U> &p) { return str >> p.f >> p.s; }
template<class T> inline istream& operator>>(istream& str, vector<T> &a) { for (auto &i : a) str >> i; return str; }

signed main() {
    FAST; FIXED; RANDOM;
    int n;
    cin >> n;
    for (int i = 0; i < n; ++i) {
        for (int j = i + 1; j < n; ++j)
            cout << i + 1 << ' ';
        cout << '\n';
    }
    return 0;
}