AT_arc207_b [ARC207B] Balanced Neighbors 2

You are given an integer $ N $ . Determine whether there exists a simple connected undirected graph with $ N $ vertices numbered $ 1 $ to $ N $ that satisfies the following condition, and if it exists, show one such graph. - There exists an integer $ X $ such that for any vertex $ v $ , the sum of the numbers of all vertices other than $ v $ that can be reached from $ v $ by traversing an edge once or twice is $ X $ .

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

If there does not exist a simple connected undirected graph with $ N $ vertices satisfying the condition in the problem statement, print `-1`. If it exists, print the number of edges $ M $ on the first line. On the $ i $ -th of the following $ M $ lines, print two integers. These represent the vertex numbers of the endpoints of the $ i $ -th edge. Any constructed graph that satisfies the condition will be accepted.

### Sample Explanation 2 If there does not exist a graph satisfying the condition, print `-1`. ### Constraints - $ 2 \le N \le 200 $ - All input values are integers.