private sealed record PathPoint(int X, int Y, int Direction, int Moves);

public static int MinimumMoves(List<string> grid, int startX, int startY, int goalX, int goalY)
{
    var moveDistances = Enumerable.Range(0, grid.Count).Select(_ => Enumerable.Repeat(int.MaxValue, grid.Count).ToArray()).ToArray();
    var directions = new List<(int Dx, int Dy)> { (-1, 0), (0, -1), (0, 1), (1, 0) };
    var pathQueue = new Queue<PathPoint>();
    var results = new List<int>();

    moveDistances[startX][startY] = 0;
    pathQueue.Enqueue(new PathPoint(startX, startY, -1, 0));

    while (pathQueue.TryDequeue(out var path))
    {
        if (path.X == goalX && path.Y == goalY)
        {
            results.Add(path.Moves);
        }

        for (var i = 0; i < directions.Count; i++)
        {
            var (x, y) = (path.X + directions[i].Dx, path.Y + directions[i].Dy);
            if (x >= 0 && x < grid.Count && y >= 0 && y < grid.Count && grid[x][y] != 'X')
            {
                var moves = path.Moves + (i == path.Direction ? 0 : 1);
                if (moves < moveDistances[x][y])
                {
                    moveDistances[x][y] = moves;
                    pathQueue.Enqueue(new PathPoint(x, y, i, moves));
                }
            }
        }
    }

    return results.Min();
}