Santa was not benevolent with his presents this year. Anthony is an unfortunate little boy who received a puzzle for Christmas. The puzzle is shaped like an
by
grid where the top left corner is represented by
and the bottom-right corner is represented by
. A marble starts at
and must make its way to
. Anthony can tilt the puzzle, allowing the marble to move to an adjacent cell, using
second of time. However, in this puzzle, all but
cells are blocked by magnets which repel the marble. This means that there may not be an empty direct path from
to
. To circumvent this, Anthony can slide a magnet into another adjacent empty cell using
second of time, (effectively swapping the positions of the empty cell with the magnet cell). It is guaranteed that
is originally empty. Because he isn't very dexterous, Anthony can only do one of the two moves (tilting the puzzle or moving a magnet) at any given time.
Anthony was promised a reward from Santa if he finishes the puzzle. Wanting to get his present as soon as possible and being technologically inept, he hired you to create a program to find the shortest amount of time he will take to complete the puzzle.
Note: adjacent cells must share a common side.
Input Specification
The first line of input will consist of five positive integers,
,
,
,
,
, representing the size of the grid, the starting row of the marble, the starting column of the marble, the destination row, and the destination column.
The next 2 lines each contain a pair of space-separated positive integers representing the original positions of the empty cells.
Output Specification
Output a single integer, the minimum amount of time required to complete the puzzle.
Constraints
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
is originally empty and is one of the two inputted empty cells.
Sample Input
Copy
3 1 1 3 3
1 1
2 2
Sample Output
Copy
11
Sample Explanation
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