Nauuo and Chess

 https://codeforces.com/contest/1173/problem/B

题意：在m*m的棋盘上放置n个棋子，使得任意两个棋子的坐标和编号满足,求最小m及其n个棋子的放置位置

题解：构造+思维

1、

1 2 0 0 * 0

0 3 4 0 * 0
 
0 0 5 6 * 0
 
* * * * * 0
0 0 0 0 0 n

或者

1 2 0 0 * 0

0 3 4 0 * 0
 
0 0 5 6 * 0
 
* * * * * n
0 0 0 0 0 0

2、m=(n+2)/2

证明：

/*
*@Author:   STZG
*@Language: C++
*/
#include <bits/stdc++.h>
#include<iostream>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<deque>
#include<stack>
#include<cmath>
#include<list>
#include<map>
#include<set>
//#define DEBUG
#define RI register int
#define endl "\n"
using namespace std;
typedef long long ll;
//typedef __int128 lll;
const int N=100000+10;
const int M=100000+10;
const int MOD=1e9+7;
const double PI = acos(-1.0);
const double EXP = 1E-8;
const int INF = 0x3f3f3f3f;
int t,n,m,k,p,l,r,u,v;
int ans,cnt,flag,temp,sum;
int a[N];
char str;
struct node{};
int main()
{
#ifdef DEBUG
	freopen("input.in", "r", stdin);
	//freopen("output.out", "w", stdout);
#endif
    //ios::sync_with_stdio(false);
    //cin.tie(0);
    //cout.tie(0);
    //scanf("%d",&t);
    //while(t--){
    scanf("%d",&n);
    cout<<(n+2)/2<<endl;
    for(int i=1;i<=n;i++){
        cout<<(i+1)/2<<" "<<(i+2)/2<<endl;
    }
    //}

#ifdef DEBUG
	printf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC);
#endif
    //cout << "Hello world!" << endl;
    return 0;
}