Description

You're moving your game character to pick an item in the following map:

rect_1.png

The map is a combination of rectangles whose sides are parallel to the X-axis and Y-axis. The character will move along the boundary of this map (the lines in bold).

When these rectangles overlap, your character will move along the outermost boundary.

rect_2.png

Two different rectangles don't share either X-coordinates or Y-coordinates.

rect_4.png

For example, two different rectangles don't share either vertices or sides, as illustrated above.

The map will never be divided into two, as illustrated below:

rect_3.png

No rectangle will be enveloped completely inside another rectangle, as illustrated below:

rect_7.png

Suppose parameters rectangle, characterX, characterY, itemX, and itemY are given, where rectangle is a two-dimensional array representing the map, characterX and characterY the initial location of your character, and itemX and itemY the location of item. Please write a function solution that returns the minimum distance that your character will travel to get the item.

Constraints
  • The length of each column in rectangle is between 1 and 4.
  • Each element of rectangle is the coordinate information [bottom-left x, bottom-left y, top-right x, top-right y] of each rectangle.
    • The value of each coordinate is a natural number between 1 and 50.
    • Two different rectangles don't share x-coordinates or y-coordinates.
    • All given rectangles will meet the conditions described in the prompt above.
  • characterX and characterY are natural numbers between 1 and 50.
    • There will be a point on the outer boundary of the map.
  • itemX and itemY are natural numbers between 1 and 50.
    • There will be a point on the outer boundary of the map.
  • The initial character location and the item location are never identical.

Example
rectangle characterX characterY itemX itemY result
[[1,1,7,4],[3,2,5,5],[4,3,6,9],[2,6,8,8]] 1 3 7 8 17
[[1,1,8,4],[2,2,4,9],[3,6,9,8],[6,3,7,7]] 9 7 6 1 11
[[1,1,5,7]] 1 1 4 7 9
[[2,1,7,5],[6,4,10,10]] 3 1 7 10 15
[[2,2,5,5],[1,3,6,4],[3,1,4,6]] 1 4 6 3 10

Example #1

rect_5.png

The initial character location is (1, 3). The item location is (7, 8). The minimum distance travel is depicted above.

Example #2

rect_6.png

The initial character location is (9, 7). The item location is (6, 1). The minimum distance travel is depicted above.

Example #3

rect_8.png

The initial character location is (1, 1). The item location is (4, 7). The minimum distance travel is depicted above.

Example #4, #5

Omitted

Result Stop
Result of [Run] or [Submit] will be displayed here