The problem is an over simplification of the flow of liquid. $-$ A terrain is given as a grid of cells of random elevations. The grid is always odd sized and is always a square. $-$ A liquid is poured at the central cell. Water can flow only north$-$south or east$-$west; not diagnonally. $-$ At the first step, the water level is the same as the central cell. $-$ Water from one cell flows to a neighbouring cell if the level of water is equal to greater than the elevation of the neighbouring cell. $-$ When the water flows to the neighbouring cell, the level of water is maintained. $-$ If the water cannot flow to any new cell, the water level rises. $-$ The simulation stops when the water reaches the end of the domain. $-$ The output consists of the domain represented by$.$ and $W$ representing dry and wet terrain.

Below is an example

Input Format

$\{\begin{array}{c}\text{:}167931780416954275\end{array}$

Water level and location of water:

Current water level: $172$

Water level and location of water:

Current water level: $172$

$...$W$..$

$.$W$...$

$q,$

$q,$

$q,$

Current water level: $172$

$q,$

$q,$

$q,$

$.$W$..$

The problem is an over simplification of the flow of liquid. $-$ A terrain is given as a grid of cells of random elevations. The grid is always odd sized and is always a square. $-$ A liquid is poured at the central cell. Water can flow only north$-$south or east$-$west; not diagnonally. $-$ At the first step, the water level is the same as the central cell. $-$ Water from one cell flows to a neighbouring cell if the level of water is equal to greater than the elevation of the neighbouring cell. $-$ When the water flows to the neighbouring cell, the level of water is maintained. $-$ If the water cannot flow to any new cell, the water level rises. $-$ The simulation stops when the water reaches the end of the domain. $-$ The output consists of the domain represented by $.$ and $W$ representing dry and wet terrain.

Below is an example

Input Format

$\{\begin{array}{c}\text{:}167931780416954275\end{array}$

Water level and location of water:

Current water level: $172$

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