Problem: 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

Solution (in PYTHON3):

Solution:
import math

I = lambda: list(map(int, input().split()))
n, d, a = I()
l = []
for _ in range(n):
	x, y = I()
	l.append([x,y])
l.sort()

j = 0
limit = []
for i in range(n):
	while l[j][0] - l[i][0] <= 2*d:
		j+=1
		if j == n: break
	j-=1
	limit.append(j)

ans = 0
num=[0]*(n+1)
cnt=0
for i in range(n):
	l[i][1]-=(ans-cnt)*a
	damage_cnt=max(0,(l[i][1]-1)//a + 1)
	ans+=damage_cnt
	num[limit[i]]+=damage_cnt
	cnt+=num[i]
print(ans)