You are given a square grid with some cells open (.) and some blocked (X). Your playing piece can move along any row or column until it reaches the edge of the grid or a blocked cell. Given a grid, a start and a goal, determine the minmum number of moves to get to the goal.

Example.

$grid=[\text{'...'},\text{'.X.'},...\text{'}]$

$start X=0$

$start Y=0$

$goal X=1$

$goal Y=2$

The grid is shown below:

...
.X.
...

The starting position $(start X,start Y)=(0,0)$ so start in the top left corner. The goal is $(goal X,goal Y)=(1,2)$. The path is $(0,0)\to(0,2)\to(1,2)$. It takes $2$ moves to reach the goal.

Function Description

Complete the minimumMoves function in the editor.

minimumMoves has the following parameter(s):

string grid[n]: an array of strings that represent the rows of the grid
int startX: starting X coordinate
int startY: starting Y coordinate
int goalX: ending X coordinate
int goalY: ending Y coordinate

Returns

int: the minimum moves to reach the goal

Input Format

The first line contains an integer $n$, the size of the array grid.

Each of the next $n$ lines contains a string of length $n$.

The last line contains four space-separated integers, $startX,$start $\mathrm{Y}$ goalX, goalY

Constraints

$1\leq n\leq100$
$0\leq$startY,goalX,goalY<n

Sample Input
STDIN FUNCTION
----- --------
3 grid[] size n = 3
.X. grid = ['.X.','.X.', '...']
.X.
...
0 0 0 2 startX = 0, startY = 0, goalX = 0, goalY = 2

Sample Output
3

Explanation

Here is a path that one could follow in order to reach the destination in $3$ steps:

$(0,0)\to(2,0)\to(2,2)\to(0,2)$.

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