Magic Odd Square （思维+构造）

Find an n × n matrix with different numbers from 1 to n2, so the sum in each row, column and both main diagonals are odd.

Input

The only line contains odd integer n (1 ≤ n ≤ 49).

Output

Print n lines with n integers. All the integers should be different and from 1 to n2. The sum in each row, column and both main diagonals should be odd.

Examples

Input

1

Output

1

Input

3

Output

2 1 4
3 5 7
6 9 8

这个题在中间的菱形区域是奇数，其余为偶数

代码：

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
#include<queue>
#include<stack>
#include<set>
#include<map>
#include<vector>
#include<cmath>

const int maxn=3e5+5;
typedef long long ll;
using namespace std;

int a[maxn];
int b[maxn];
int Map[200][200];
int main()
{
	int n;
	cin>>n;
	memset(Map,0,sizeof(Map));
	int cnt1=0;
	int cnt2=0;
	for(int t=1;t<=n*n;t++)
	{
		if(t%2==0)
		{
			a[cnt1++]=t;
		}
		else
		{
			b[cnt2++]=t;
	    }
	}
	int cnt3=0;
	for(int t=0;t<n;t++)
	{
		for(int j=0;j<n;j++)
		{
			if(j>=n/2-t&&j<=t+n/2&&j<=n-1+n/2-t&&j>=t-n/2)
			{
				Map[t][j]=b[cnt3];
				cnt3++;
			}
		}
	}
	int cnt4=0;
	for(int t=0;t<n;t++)
	{
		for(int j=0;j<n;j++)
		{
			if(Map[t][j]==0)
			{
				Map[t][j]=a[cnt4];
				cnt4++;
			}
		}
	}
	for(int t=0;t<n;t++)
	{
		for(int j=0;j<n;j++)
		{
			cout<<Map[t][j]<<" ";
		}
		cout<<endl;
	}
}