There is an ((n+2) \times (n+2)) grid, where both coordinates range from (0) to (n+1) inclusive. The outermost cells of the grid are all obstacle cells. In addition, there are (m) more obstacle cells in the grid. The (i)-th obstacle cell is located at ((x_i, y_i)). It is guaranteed that all obstacles (including the outer boundary cells) are 4-connected. That is, you can move between any two obstacle cells by moving up, down, left, or right through other obstacle cells. Little L is walking in this maze. He cannot step into any obstacle cell at any time. If Little L is at position ((x, y)), he can make the following moves: Move orthogonally to an adjacent cell ((x+1,y)), ((x-1,y)), ((x,y+1)), or ((x,y-1)) with a cost of (2). Move diagonally to an adjacent cell ((x+1,y+1)), ((x+1,y-1)), ((x-1,y+1)), or ((x-1,y-1)) with a cost of (3). There are (q) queries. For each query, you are given a starting point and an ending point. You need to find the minimum total cost for Little L to travel from the starting point to the ending point. If it is impossible to reach the ending point, output (-1). The first line of the input contains three integers (n), (m), and (q) ((1 \le n \le 10^5), (1 \le m, q \le 3 \cdot 10^5)). The next (m) lines each contain two integers (x_i) and (y_i) — the coordinates of the (i)-th obstacle cell. It is guaranteed that all obstacle coordinates are distinct, and that all obstacles (including the outer boundary cells) are 4-connected. The next (q) lines each contain four integers (s_x), (s_y), (t_x), and (t_y) — a query with starting point ((s_x, s_y)) and ending point ((t_x, t_y)). It is guaranteed that neither ((s_x,s_y)) nor ((t_x,t_y)) is an obstacle. For each query, output a single integer — the minimum cost to travel from the starting point to the ending point. Or print (-1) if it is impos