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:
#!/usr/bin python3
# -*- coding: utf-8 -*-

from bisect import bisect_left, bisect_right

n, d, a = map(int, input().split())
x = []
xh = dict()
for _ in range(n):
    xi, hi = map(int, input().split())
    x.append(xi)
    xh[xi] = hi
x.sort()

l = 0
ret = 0
ai = [0] * (n+1)
anow = 0
while l < n:
    xl = x[l]
    hl = xh[xl]
    anow += ai[l]
    hl -= a * anow
    if hl > 0:
        r = bisect_right(x, xl+2*d)
        k = (hl+(a-1))//a
        ret += k
        anow += k
        ai[r] -= k
    l += 1
print(ret)