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=[int(x) for x in input().split()]
xh = [[int(x) for x in input().split()] for _ in range(N)]
xh = sorted(xh)
r=0
l=0
ans = 0
mi = 10**9
d = [0]*(N+1)
for l in range(N):
  if d[l]<xh[l][1]:
    la = (xh[l][1]-d[l]+A-1)//A
    for _ in range(N):
      if l<N and r<N and 2*D>=xh[r][0]-xh[l][0]:
        r+=1
      else:
        break
    ans += la
    d[l]+=la*A
    d[r]-=la*A
  d[l+1]+=d[l]
print(ans)