Rainbow

题目描述

Given a positive integer $n$. Construct an $n \times n$ matrix $A$ with $n^2$ elements $A_{i,j}$($i,j \in \{1,2,\dots,n\}$), such that:

• $\forall x \in \{1,2,\dots,n^2\}$, there exists a unique pair of $(i,j)$ such that $A_{i,j}=x$.
• $\forall i,j \in \{1,2,\dots,n\}$, $A_{i,j} \neq i \times j$.

输入格式

The input consists of one line, containing a single integer $n$($1 \le n \le 500$).

输出格式

If there is no solution, output one line containing a single number $-1$.

Otherwise, the output should consist of $n$ lines, each contains $n$ positive numbers. The $j$-th number of line $i$ is $A_{i,j}$.

If there are multiple solutions, you may output any of them.

样例输入 #1

3

样例输出 #1

3 8 4
5 2 1
9 7 6