Problem Statement

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

Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
$\hspace{0.45cm}\vdots$
x_N y_N

Output

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

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.

Sample Input 1

3
1 1
2 1
1 2

Sample Output 1

2

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.

Sample Input 2

10
414598724 87552841
252911401 309688555
623249116 421714323
605059493 227199170
410455266 373748111
861647548 916369023
527772558 682124751
356101507 249887028
292258775 110762985
850583108 796044319

Sample Output 2

10

It is best to keep all 7's.

见题面 Input 部分

见题面 Output 部分