Open air#4607
You are given a full set of dominoes, where each domino has two numbers from to written on it ( is even). Each unordered pair of numbers appears exactly once. It is easy to count that the total number of dominoes in the set is \frac{(N+1)(N+2)}{2}.
Arrange all dominoes horizontally into N+1 rows in such a way that the sum of the numbers on the dominoes in each row is the same. It is guaranteed that this is always possible.
The only line contains an even integer (2 \leq N \leq 100).
Output N+1 lines with N+2 numbers in each: a_1, b_1, a_2, b_2, \ldots, a_k, b_k, where k = \frac{N+2}{2} in each row, and each pair a_i, b_i corresponds to a domino. Each domino must be used exactly once. The order of the numbers on each domino can be arbitrary. If there are multiple solutions, you may output any of them.
Example 1