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50996 - Checkers - the shortest path

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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Prepared by Ibrahim Mesecan.

Checkers - the shortest path

Checkers is a board game, in which the pieces can move only in diagonals. Refer to the image for orientation and possible moves.

Question:
Write a program that finds the fastest move from a given (xf, yf) coordinate to the destination. Note: Assume that your pieces cannot jump over the given obstacles.

Input specification
Firstly, you will be first given 2 integers

  • The size of the board (n) where the board is an nxn matrix and 1 ≤ n ≤ 250
  • The number of cells (m) occupied by other pieces where 0 ≤ m ≤ 5000
Then in the following line you will be given four integers initial (xi, yi) starting position and the destination (xf, yf). Then, in the following m lines you will be given (x,y) coordinates of m occupied cells.

Output specification
Show the minimum number of moves that the pieces can reach to the destination. Show -1, if it cannot reach to the destination.

Sample Input I
5 5
1 1 3 5
3 1
1 3
1 2
4 4
3 2
Sample Input II
4 2
1 1 2 4
4 1
2 2
Sample Output I  
4
Sample Output II
-1


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