Score : $800$ points

Problem Statement

Takahashi is doing a research on sets of points in a plane. Takahashi thinks a set $S$ of points in a coordinate plane is a good set when $S$ satisfies both of the following conditions:

• The distance between any two points in $S$ is not $\sqrt{D_1}$.
• The distance between any two points in $S$ is not $\sqrt{D_2}$.

Here, $D_1$ and $D_2$ are positive integer constants that Takahashi specified.

Let $X$ be a set of points $(i,j)$ on a coordinate plane where $i$ and $j$ are integers and satisfy $0 \leq i,j < 2N$.

Takahashi has proved that, for any choice of $D_1$ and $D_2$, there exists a way to choose $N^2$ points from $X$ so that the chosen points form a good set. However, he does not know the specific way to choose such points to form a good set. Find a subset of $X$ whose size is $N^2$ that forms a good set.

Constraints

• $1 \leq N \leq 300$
• $1 \leq D_1 \leq 2 \times 10^5$
• $1 \leq D_2 \leq 2 \times 10^5$
• All values in the input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $D_1$ $D_2$

Output

Print $N^2$ distinct points that satisfy the condition in the following format:

$x_1$ $y_1$

$x_2$ $y_2$

:

$x_{N^2}$ $y_{N^2}$

Here, $(x_i,y_i)$ represents the $i$-th chosen point. $0 \leq x_i,y_i < 2N$ must hold, and they must be integers. The chosen points may be printed in any order. In case there are multiple possible solutions, you can output any.

2 1 2

0 0
0 2
2 0
2 2

Among these points, the distance between $2$ points is either $2$ or $2\sqrt{2}$, thus it satisfies the condition.

3 1 5

0 0
0 2
0 4
1 1
1 3
1 5
2 0
2 2
2 4