There are $N$ 7's drawn in the first quadrant of a plane. The $i$-th 7 is a figure composed of a segment connecting $(x_{i}-1,y_{i})$ and $(x_i,y_i)$, and a segment connecting $(x_i,y_{i}-1)$ and $(x_i,y_i)$. You can choose zero or more from the $N$ 7's and delete them. What is the maximum possible number of 7's that are wholly visible from the origin after the optimal deletion? Here, the $i$-th 7 is wholly visible from the origin if and only if: - the interior (excluding borders) of the quadrilateral whose vertices are the origin, $(x_{i}-1,y_i)$, $(x_i,y_i)$, $(x_i,y_{i}-1)$ does not intersect with the other 7's.

Input is given from Standard Input in the following format: > $N$\ > $x_1 \quad y_1$\ > $x_2 \quad y_2$\ > $\vdots$\ > $x_N \quad y_N$ #### Constraints - $1 \leq N \leq 2 \times 10^5$ - $1 \leq x_i, y_i \leq 10^9$ - $(x_i, y_i) \neq (x_j, y_j)$ $(i \neq j)$ - All values in input are integers.

Print the maximum possible number of 7's that are wholly visible from the origin.

***For Sample #1:*** If the first 7 is deleted, the other two 7's ― the second and third ones ― will be wholly visible from the origin, which is optimal. If no 7's are deleted, only the first 7 is wholly visible from the origin. ***For Sample #2:*** It is best to keep all 7's.

AtCoder [ABC225E]