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

n, d, a = map(int, input().split())
l = [list(map(int, input().split())) for _ in range(n)]
l.sort()
q = []
index = 0
ans = 0
dmg = 0
for i in range(n):
    while index < len(q) and q[index][0] < l[i][0]:
        dmg -= q[index][1]
        index += 1
    if l[i][1] > dmg:
        times = (l[i][1]-dmg)//a if (l[i][1]-dmg)%a == 0 else (l[i][1]-dmg)//a+1
        ans += times
        q.append((l[i][0]+2*d, a*times))
        dmg += a*times
print(ans)