Score : $200$ points

Problem Statement

In a factory, there are $N$ robots placed on a number line. Robot $i$ is placed at coordinate $X_i$ and can extend its arms of length $L_i$ in both directions, positive and negative.

We want to remove zero or more robots so that the movable ranges of arms of no two remaining robots intersect. Here, for each $i$ ($1 \leq i \leq N$), the movable range of arms of Robot $i$ is the part of the number line between the coordinates $X_i - L_i$ and $X_i + L_i$, excluding the endpoints.

Find the maximum number of robots that we can keep.

Constraints

• $1 \leq N \leq 100,000$
• $0 \leq X_i \leq 10^9$ ($1 \leq i \leq N$)
• $1 \leq L_i \leq 10^9$ ($1 \leq i \leq N$)
• If $i \neq j$, $X_i \neq X_j$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$X_1$ $L_1$

$X_2$ $L_2$

$\vdots$

$X_N$ $L_N$

Output

Print the maximum number of robots that we can keep.

4
2 4
4 3
9 3
100 5

3

By removing Robot $2$, we can keep the other three robots.

2
8 20
1 10

1

5
10 1
2 1
4 1
6 1
8 1

5