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.

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

def bit_add(bit, i, x):
    i += 1
    while i <= len(bit):
        bit[i - 1] += x
        i += i & -i


def bit_sum(bit, i):
    result = 0
    i += 1
    while i > 0:
        result += bit[i - 1]
        i -= i & -i
    return result


def main():
    from sys import stdin
    readline = stdin.readline
    N, D, A = map(int, readline().split())
    XH = [list(map(int, readline().split())) for _ in range(N)]

    XH.sort()
    result = 0
    bit = [0] * (N + 1)
    for i in range(N):
        x, h = XH[i]
        h -= bit_sum(bit, i)
        if h <= 0:
            continue
        c = (h + A - 1) // A
        result += c
        bit_add(bit, i, c * A)

        ok = i
        ng = N
        while ng - ok != 1:
            m = ok + (ng - ok) // 2
            if XH[m][0] <= x + 2 * D:
                ok = m
            else:
                ng = m
        bit_add(bit, ng, -c * A)
    print(result)


main()