Silver Fox vs Monster

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

inputFormat

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

outputFormat

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

样例

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

5