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
# -*- coding: utf-8 -*-

import sys

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
MOD = 10 ** 9 + 7

N = INT()

G = list2d(N, N, 0)
A = list(range(N))

def rec(li, lv):
    n = len(li)
    # 頂点が1つ以下になったら終了
    if n <= 1:
        return
    # 頂点集合を半分に分けて、2部グラブにする
    li1 = li[:n//2]
    li2 = li[n//2:]
    for u in li1:
        for v in li2:
            G[u][v] = lv
    # 半分にした集合を再帰的に処理する
    rec(li1, lv+1)
    rec(li2, lv+1)
    return

rec(A, 1)

ans = []
for i in range(N):
    row =[]
    for j in range(i+1, N):
        row.append(G[i][j])
    ans.append(row)

for row in ans:
    print(*row)
