$n$ sprinklers are
installed in a horizontal strip of grass $l$ meters long and $w$ meters wide. Each sprinkler is
installed at the horizontal center line of the strip. For each
sprinkler we are given its position as the distance from the
left end of the center line and its radius of operation.
What is the minimum number of sprinklers to turn on in order
to water the entire strip of grass?
Input
Input consists of a number of cases. The first line for each
case contains integer numbers $n$, $l$ and $w$ with $1 \le n \le 10\, 000$, $1 \le l \le 10^7$, and $1 \le w \le 100$. The next
$n$ lines contain two
integers giving the position $x$ ($0
\le x \le 10^7$) and radius of operation $r$ ($1
\le r \le 1\, 000$) of a sprinkler.
The picture above illustrates the first case from the sample
input.
Output
For each test case output the minimum number of sprinklers
needed to water the entire strip of grass. If it is impossible
to water the entire strip output $1$.
Sample Input 1 
Sample Output 1 
8 20 2
5 3
4 1
1 2
7 2
10 2
13 3
16 2
19 4
3 10 1
3 5
9 3
6 1
3 10 1
5 3
1 1
9 1

6
2
1
