Minimum Knight Moves on an n x n Board (Bounded Grid Variant)

Problem: Minimum Knight Moves on a Bounded n x n Board You are given a finite n x n chessboard. A knight can move from (x, y) to any of the 8 positions: (x+2, y+1), (x+2, y-1) (x-2, y+1), (x-2, y-1) (x+1, y+2), (x+1, y-2) (x-1, y+2), (x-1, y-2) Moves that go outside the board are not allowed. Given start = (sx, sy) and target = (tx, ty) (both within the board), return the minimum number of moves needed to reach target from start, or -1 if it is impossible. Input (stdin) One line with 5 integers: n sx sy tx ty Output (stdout) Print one integer: the minimum number of moves (or -1 if unreachable). Constraints 1 <= n <= 2000 0 <= sx, sy, tx, ty < n Examples Input: 8 0 0 7 7 Output: 6 Input: 4 0 0 3 3 Output: 2 Input: 3 0 0 2 2 Output: 4 Input: 2 0 0 1 1 Output: -1 Input: 1 0 0 0 0 Output: 0 Example Input 8 0 0 7 7 Output 6