@1kri 提供一组 $n > 1000$ 时答案为 $4$ 的数据。

数据生成器：

#include <iostream>
#include <cstdio>
using namespace std;
int main ()
{
	//freopen (".in","r",stdin);
	//freopen ("line.in","w",stdout);
	int n = 15000;
	cout<<1<<endl;
	cout<<n * 4 + 8<<endl;
	for (int i = 1;i <= n;++i) cout<<i<<" "<<n + 2<<endl;
	for (int i = 1;i <= n;++i) cout<<n + 2<<" "<<i<<endl;
	for (int i = 1;i <= n;++i) cout<<n + 2<<" "<<n + 3 + i<<endl;
	for (int i = 1;i <= n;++i) cout<<n + 3 + i<<" "<<n + 2<<endl;
	cout<<n + 1<<" "<<n + 1<<endl<<n + 2<<" "<<n + 1<<endl<<n + 3<<" "<<n + 1<<endl;
	cout<<n + 1<<" "<<n + 2<<endl<<n + 3<<" "<<n + 2<<endl;
	cout<<n + 1<<" "<<n + 3<<endl<<n + 2<<" "<<n + 3<<endl<<n + 3<<" "<<n + 3<<endl;
	return 0;
}