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.

Examples

Input

3 3 2
1 2
5 4
9 2

Output

2

Input

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

Output

5

Input

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000

Output

3000000000

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