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D. Prime Graph
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

The input consists of a single integer $n$ ($3 \leq n \leq 1\,000$) — the number of vertices.

Output

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 $m$ ($2 \leq m \leq \frac{n(n-1)}{2}$) — the number of edges in the graph. Then, print $m$ lines, the $i$-th of which containing two integers $u_i$, $v_i$ ($1 \leq u_i, v_i \leq n$) — 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.

Examples
Input
4

Output
5
1 2
1 3
2 3
2 4
3 4
Input
8

Output
13
1 2
1 3
2 3
1 4
2 4
1 5
2 5
1 6
2 6
1 7
1 8
5 8
7 8

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. 