Codeforces Round #564 (Div. 2)B

B. Nauuo and Chess

题目链接：http://codeforces.com/contest/1173/problem/B

题目

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 m×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 (ri,ci), while the following rule is satisfied: for all pairs of pieces i and j, |ri−rj|+|ci−cj|≥|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≤n≤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 ri and ci (1≤ri,ci≤m) — the coordinates of the i-th chess piece.
If there are multiple answers, print any.

Example

input

2

output

2
1 1
1 2

题意

给你一个数，你在方格中放这1~n这些数，使得任意两个数a->b在方格中走的格数大于等于|a-b|的值

输出1~n每个数的位置

思路

给你一个表格即可发现规律

1	2
	3	4
		5	6

行走路径为先向下再向右，两数之间步数与差值都相等

#include<bits/stdc++.h>
using namespace std;
int main()
{

    int n;
    cin>>n;
    cout<<n/+<<endl;
    for(int i=;i<=n;i++)
    {
        cout<<(i+)/<<' '<<i/+<<endl;
    }

    return ;
}