write a go solution for Description:
Every person likes prime numbers. Alice is a person, thus she also shares the love for them. Bob wanted to give her an affectionate gift but couldn't think of anything inventive. Hence, he will be giving her a graph. How original, Bob! Alice will surely be thrilled!

When building the graph, he needs four conditions to be satisfied:

- It must be a simple undirected graph, i.e. without multiple (parallel) edges and self-loops.
- The number of vertices must be exactly n — a number he selected. This number is not necessarily prime.
- The total number of edges must be prime.
- The degree (i.e. the number of edges connected to the vertex) of each vertex must be prime.

Below is an example for n=4. The first graph (left one) is invalid as the degree of vertex 2 (and 4) equals to 1, which is not prime. The second graph (middle one) is invalid as the total number of edges is 4, which is not a prime number. The third graph (right one) is a valid answer for n=4.

Note that the graph can be disconnected.

Please help Bob to find any such graph!

Input Format:
The input consists of a single integer n (3<=n<=1,000) — the number of vertices.

Output Format:
If there is no graph satisfying the conditions, print a single line containing the integer -1.

Otherwise, first print a line containing a prime number m (2<=m<=n(n-1)/2) — the number of edges in the graph. Then, print m lines, the i-th of which containing two integers u_i, v_i (1<=u_i,v_i<=n) — meaning that there is an edge between vertices u_i and v_i. The degree of each vertex must be prime. There must be no multiple (parallel) edges or self-loops.

If there are multiple solutions, you may print any of them.

Note that the graph can be disconnected.

Note:
The first example was described in the statement.

In the second example, the degrees of vertices are [7,5,2,2,3,2,2,3]. Each of these numbers is prime. Additionally, the number of edges, 13, is also a prime number, hence both conditions are satisfied.. Output only the code with no comments, explanation, or additional text.