write a go solution for Description:
Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a mxm chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|>=|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input Format:
The only line contains a single integer n (1<=n<=1000) — the number of chess pieces for the game.

Output Format:
The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1<=r_i,c_i<=m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Note:
In the first example, you can't place the two pieces on a 1x1 chessboard without breaking the rule. But you can place two pieces on a 2x2 chessboard like this:

In the second example, you can't place four pieces on a 2x2 chessboard without breaking the rule. For example, if you place the pieces like this:

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3x3 chessboard, you can place four pieces like this:. Output only the code with no comments, explanation, or additional text.