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:

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

Sample Input 1

2

Sample Output 1

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 $3$.