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 b$).$ and W representing dry and wet terrain.

Below is an example

Input Format

$\{\begin{array}{c}\text{:}\{\begin{array}{c}\text{:}780416954\\ 275\end{array}\end{array}$

Water level and location of water:

Current water level: $172$

$...$W$...$

$...$W$...$

Current water level

$$ : $174$ Reached edge, exiting. Solution:

Output Format

$..$W$...$

$..$WW$...$

$.$WW$....$

$.$W$....$

Constraints: First line of the input has dimension $n$ of $(nxn)$ matrix. Followed by the matrix itself as shown below in the sample input.