Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Nauuo and Chess

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputNauuo is a girl who loves playing chess.

One day she invented a game by herself which needs $$$n$$$ chess pieces to play on a $$$m\times m$$$ 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 $$$j$$$, $$$|r_i-r_j|+|c_i-c_j|\ge|i-j|$$$. 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

The only line contains a single integer $$$n$$$ ($$$1\le n\le 1000$$$) — the number of chess pieces for the game.

Output

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 $$$c_i$$$ ($$$1\le r_i,c_i\le m$$$) — the coordinates of the $$$i$$$-th chess piece.

If there are multiple answers, print any.

Examples

Input

2

Output

2 1 1 1 2

Input

4

Output

3 1 1 1 3 3 1 3 3

Note

In the first example, you can't place the two pieces on a $$$1\times1$$$ chessboard without breaking the rule. But you can place two pieces on a $$$2\times2$$$ chessboard like this:

In the second example, you can't place four pieces on a $$$2\times2$$$ 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 $$$3\times3$$$ chessboard, you can place four pieces like this:

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/21/2021 08:17:07 (j2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|