Prime Graph

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

The input consists of a single integer n (3 ≤ n ≤ 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 ≤ 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.

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.

inputFormat

Input

The input consists of a single integer n (3 ≤ n ≤ 1 000) — the number of vertices.

outputFormat

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 ≤ 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.

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.

样例

4

5
1 2
2 3
3 4
4 1
1 3

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