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:
n, d, a = map(int, input().split())

D = True

pos = []
pos1 = []

for i in range(n):
	x, h = map(int, input().split())
	pos.append((x, h))

pos.sort(key=lambda x: x[0])

bombs = 0
damage = 0
y, z = 0, 0


while y < n:
	x0 = pos[y][0]
	try:
		x1 = pos1[z][0]
	except IndexError:
		x1 = 1e16
	if x0 <= x1:
		health = pos[y][1]
		health -= damage
		number = max(0, (health-1) // a + 1)
		bombs += number
		damage += number*a
		pos1.append((x0+2*d, number*a))
		y+=1
	else:
		damage -= pos1[z][1]
		z += 1
	

print(bombs)