Score : $100$ points

Problem Statement

There are $N$ persons, conveniently numbered $1$ through $N$. They will take 3y3s Challenge for $N-1$ seconds.

During the challenge, each person must look at each of the $N-1$ other persons for $1$ seconds, in some order.

If any two persons look at each other during the challenge, the challenge ends in failure.

Find the order in which each person looks at each of the $N-1$ other persons, to be successful in the challenge.

Constraints

• $2 \leq N \leq 100$

Input

The input is given from Standard Input in the following format:

$N$

Output

If there exists no way to be successful in the challenge, print -1.

If there exists a way to be successful in the challenge, print any such way in the following format:

$A_{1,1}$ $A_{1,2}$ $...$ $A_{1, N-1}$

$A_{2,1}$ $A_{2,2}$ $...$ $A_{2, N-1}$

:

$A_{N,1}$ $A_{N,2}$ $...$ $A_{N, N-1}$

where $A_{i, j}$ is the index of the person that the person numbered $i$ looks at during the $j$-th second.

Judging

The output is considered correct only if all of the following conditions are satisfied:

• $1 \leq A_{i,j} \leq N$
• For each $i$, $A_{i,1}, A_{i,2}, ... , A_{i, N-1}$ are pairwise distinct.
• Let $X = A_{i, j}$, then $A_{X, j} \neq i$ always holds.

7

2 3 4 5 6 7
5 3 1 6 4 7
2 7 4 1 5 6
2 1 7 5 3 6
1 4 3 7 6 2
2 5 7 3 4 1
2 6 1 4 5 3

2

-1