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
import bisect
n,d,a = map(int,input().split())
L = []
kyo = []
for i in range(n):
    x,h = map(int,input().split())
    L.append([x,h])
    kyo.append(x)
L.sort()
kyo.sort()
ans = 0
imos = [0]*(n+1)
cur = 0
ran = 2*d
for i in range(n):
    if imos[cur] < L[cur][1]:
        t = int(math.ceil((L[cur][1]-imos[cur])/a))
        ans += t
        imos[cur] += t*a
        lim = bisect.bisect_right(kyo, kyo[cur]+ran)
        imos[lim] -= t*a
    imos[i+1] += imos[i]
    cur += 1
print(ans)