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.

Example

Input

3


Output

1 2
1
#include <bits/stdc++.h>
 
using namespace std;
 
#define debug(a) cerr << #a << ": " << a << endl
 
typedef long long ll;
typedef pair<int, int> ii;
 
#define x first
#define y second
 
const int N = 510;

int n;

int main() {
	#ifdef LOCAL
	freopen("in", "r", stdin);
	freopen("out", "w", stdout);
	#endif
 
	cin >> n;

	for (int i = 1; i <= n - 1; i++) {
		for (int j = i + 1; j <= n; j++) {
			int k;
			for (k = 0; k < 10; k++) {
				if ((i & 1 << k) != (j & 1 << k)) break;
			}

			printf("%d ", k + 1);
		}
		
		printf("\n");
	}
 
	return 0;
}