Score : 700 points
You are given an integer N. Build an undirected graph with N vertices with indices 1 to N that satisfies the following two conditions:
It can be proved that at least one such graph exists under the constraints of this problem.
Input is given from Standard Input in the following format:
N
In the first line, print the number of edges, M, in the graph you made. In the i-th of the following M lines, print two integers a_i and b_i, representing the endpoints of the i-th edge.
The output will be judged correct if the graph satisfies the conditions.
3
2 1 3 2 3