Score : $1100$ points

Problem Statement

You are given an integer $N$.

Construct any one $N$-by-$N$ matrix $a$ that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem.

• $1 \leq a_{i,j} \leq 10^{15}$
• $a_{i,j}$ are pairwise distinct integers.
• There exists a positive integer $m$ such that the following holds: Let $x$ and $y$ be two elements of the matrix that are vertically or horizontally adjacent. Then, ${\rm max}(x,y)$ ${\rm mod}$ ${\rm min}(x,y)$ is always $m$.

Constraints

• $2 \leq N \leq 500$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print your solution in the following format:

$a_{1,1}$ $...$ $a_{1,N}$

$:$

$a_{N,1}$ $...$ $a_{N,N}$

2

4 7
23 10

• For any two elements $x$ and $y$ that are vertically or horizontally adjacent, ${\rm max}(x,y)$ ${\rm mod}$ ${\rm min}(x,y)$ is always $3$.