A higher resolution is required to access the IDE

- 115

## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Statement

## Goal

The goal of the puzzle is to apply the "divide and conquer" method in order to fill a square of side`n`with L-triominoes, this is always possible if the square has a hole at the start...

You are given the value of

`n`and the coordinates (

`x`,

`y`) of the hole, your goal is to draw all the L-triominoes in the right places!

*

**Divide and conquer method :**

Divide the square into 4 equal squares.

We are then reduced to 4 smaller problems identical to the previous one:

- One of the squares already has a hole somewhere

- Place a L-triomino in the center to create a new hole in the 3 other squares.

**Exemple**:

**Test 2 : 4x4**

+--+--+--+--+

| | | | |

+--+--+--+--+

|##| | | |

+--+--+--+--+

| | | | |

+--+--+--+--+

| | | | |

+--+--+--+--+

The hole is in top-left 2x2 square, so I have to solve 4 smaller problems...

* top-left 2x2 square with initial hole:

+--+--+ +--+--+

| | | | |

+--+--+ => +--+ +

|##| | |##| |

+--+--+ +--+--+

* top-right 2x2 square with new hole:

+--+--+ +--+--+

| | | | |

+--+--+ => +--+ +

|##| | |##| |

+--+--+ +--+--+

* bottom-left 2x2 square with new hole:

+--+--+ +--+--+

| |##| | |##|

+--+--+ => + +--+

| | | | |

+--+--+ +--+--+

* bottom-right 2x2 square with new hole:

+--+--+ +--+--+

|##| | |##| |

+--+--+ => +--+ +

| | | | |

+--+--+ +--+--+

* join the 4 squares

+--+--+--+--+ +--+--+--+--+

| | | | | | | |

+--+--+--+--+ +--+ +--+ +

|##| |##| | |##| | | |

+--+--+--+--+ => +--+--+ +--+

| |##|##| | | | | |

+--+--+--+--+ + +--+--+ +

| | | | | | | |

+--+--+--+--+ +--+--+--+--+

Input

**Line 1**: Level

`n`, for a square of side 2^

`n`

**Line 2**: coordinates (

`x`,

`y`) of the hole.

**Note**: (

Output

**1 + 2^(**: The grid of L-triominoes

`n`+ 1) lines**Hole**:

+--+

|##|

+--+

**L-triminoes**:

+--+ +--+--+ +--+--+ +--+

| | | | | | | |

+ +--+ + +--+ +--+ + +--+ +

| | | | | | | |

+--+--+ +--+ +--+ +--+--+

Constraints

1 <=

0 <=

`n`<= 30 <=

`x`,`y`<= 2^`n`- 1Example

Input

1 1 1

Output

+--+--+ | | + +--+ | |##| +--+--+

A higher resolution is required to access the IDE