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 bisect, math
N,D,A = map(int,input().split())
enemy = list(list(map(int,input().split()))for i in range(N))
enemy.sort()

damege = [0]*N

ans = 0
p = 0
while p < N:
    if p>=1:
        damege[p] += damege[p-1]
    enemy[p][1] -= damege[p]
    if enemy[p][1] <= 0:
        p += 1 
        continue
    d = math.ceil(enemy[p][1]/A)
    ans += d
    d *= A
    r = bisect.bisect_right(enemy,[enemy[p][0]+D*2,10**9+7])
    if r!=N:
        damege[r]-=d
    damege[p] += d
    p+=1
print(ans)