101535: [AtCoder]ABC153 F - Silver Fox vs Monster

Problem Statement

Silver Fox is fighting with $N$ monsters.

The monsters are standing in a row, and we can assume them to be standing on a number line. The $i$-th monster, standing at the coordinate $X_i$, has the health of $H_i$.

Silver Fox can use bombs to attack the monsters. Using a bomb at the coordinate $x$ decreases the healths of all monsters between the coordinates $x-D$ and $x+D$ (inclusive) by $A$. There is no way other than bombs to decrease the monster's health.

Silver Fox wins when all the monsters' healths become $0$ or below.

Find the minimum number of bombs needed to win.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq D \leq 10^9$
• $1 \leq A \leq 10^9$
• $0 \leq X_i \leq 10^9$
• $1 \leq H_i \leq 10^9$
• $X_i$ are distinct.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $D$ $A$
$X_1$ $H_1$
$:$
$X_N$ $H_N$

Output

Print the minimum number of bombs needed to win.

Sample Input 1

3 3 2
1 2
5 4
9 2

Sample Output 1

2

First, let us use a bomb at the coordinate $4$ to decrease the first and second monsters' health by $2$.

Then, use a bomb at the coordinate $6$ to decrease the second and third monsters' health by $2$.

Now, all the monsters' healths are $0$. We cannot make all the monsters' health drop to $0$ or below with just one bomb.

Sample Input 2

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5

Sample Output 2

5

We should use five bombs at the coordinate $5$.

Sample Input 3

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000

Sample Output 3

3000000000

Watch out for overflow.