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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from collections import deque
N=int(input())
if N%2==1:
    a=[[0 for j in range(N-i-1)] for i in range(N-1)]
    K=N//2
    #i->j(i<j)
    #a[i-1][j-i-1]
    for k in range(1,K+1):
        x=1
        for i in range(N-1):
            y,x=x,(x+k)%N
            if x==0:
                x=N
            if y==0:
                y=N
            p,q=min(x,y),max(x,y)
            #print(k,i,p,q,x,y)
            a[p-1][q-p-1]=k

    for i in range(N-1):
        for j in range(N-i-1):
            if a[i][j]==0:
                a[i][j]=K+1
    for i in range(N-1):
        print(*a[i])
else:
    K=N//2
    q=deque([i for i in range(1,N+1)])
    X=[]
    X.append(q.popleft())
    X.append(q.popleft())
    index=0
    while(len(q)>0):
        if index%2==0:
            X.append(q.pop())
        else:
            X.append(q.popleft())
        index+=1
    #print(X)
    a=[[0 for j in range(N-i-1)] for i in range(N-1)]
    for k in range(1,K+1):
        for i in range(N-1):
            x,y=(X[i]+k)%N,(X[i+1]+k)%N
            if x==0:
                x=N
            if y==0:
                y=N
            p,q=min(x,y),max(x,y)
            a[p-1][q-p-1]=k
    for i in range(N-1):
        print(*a[i])