Problem:


Score : 600 points

Problem Statement

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.

Sample Input 1

3 3 2
1 2
5 4
9 2

Sample Output 1

2

First, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.

Then, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.

Now, all the monsters' healths are 0.
We cannot make all the monsters' health drop to 0 or below with just one bomb.

Sample Input 2

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5

Sample Output 2

5

We should use five bombs at the coordinate 5.

Sample Input 3

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000

Sample Output 3

3000000000

Watch out for overflow.



Sample input:
3 3 2
1 2
5 4
9 2


Sample output:
2

Submission status: Time Limit Exceeded

Solution code:
import numpy as np
# from numba import njit
i8 = np.int64

# @njit
def solve(X, H, D):
    xi = np.empty_like(X)
    hi = np.empty_like(H)
    p = 0
    N = X.shape[0]
    for i in range(1, N):
        if X[i] > X[i - 1]:
            xi[p] = X[i - 1]
            hi[p] = H[i - 1]
            p += 1
    xi[p] = X[N - 1]
    hi[p] = H[N - 1]
    p += 1
    area = 2 * D
    res = 0
    for i in range(p):
        if hi[i] > 0:
            res += hi[i]
            for j in range(i + 1, p):
                if xi[j] - xi[i] <= area:
                    hi[j] -= hi[i]
                else:
                    break
    return res

def main(X, H, D, A):
    arg = np.lexsort((H, X))
    X = X[arg]
    H = H[arg]
    H = (H - 1) // A + 1
    print(solve(X, H, D))

if __name__ == '__main__':
    stdin = np.fromstring(open(0).read(), i8, sep=' ')
    N, D, A = stdin[:3]
    XH = stdin[3:].reshape((-1, 2)).T
    ans = main(XH[0], XH[1], D, A)