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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import sys

sys.setrecursionlimit(500000)
def input():
    return sys.stdin.readline()[:-1]

class DualSegmentTree:
    def __init__(self, n) :
        self.n = n
        self.N0 = 1 << n.bit_length()
        self.data = [0] * (self.N0*2)

    def update(self, l, r, val) :
        l += self.N0
        r += self.N0
        while l < r:
            if l & 1:
                self.data[l] = self.data[l] + val
                l += 1
            if r & 1:
                self.data[r-1] = self.data[r-1] + val
                r -= 1
            l //= 2
            r //= 2

    def query(self, i):
        i += len(self.data) // 2
        ret = self.data[i]
        while i > 0:
            i //= 2
            ret = ret + self.data[i]
        return ret




def main():
    N,D,A = list(map(int,input().split()))

    enemy = []
    for i in range(N):
        x,h = list(map(int,input().split()))
        h //= A
        enemy.append([x,h])

    enemy.sort(key=lambda x:x[0])
    def bisect(index):
        x = enemy[index][0]
        if enemy[N-1][0] <= x + 2*D:
            return N-1
        l = index
        r = N-1
        while r-l>1:
            if enemy[(r+l)//2][0] <= x + 2*D:
                l = (r+l)//2
            else:
                r = (r+l)//2
        return l

    ST = DualSegmentTree(N)

    for i in range(N):
        ST.update(i,i+1,enemy[i][1])

    count1 = 0
    for i in range(N):
        v = ST.query(i)
        if v>0:
            count1 += v
            j = bisect(i)
            ST.update(i,j+1,-v) 

    enemy = enemy[::-1]
    for i in range(N):
        enemy[i][0] = -enemy[i][0]

    ST = DualSegmentTree(N)

    for i in range(N):
        ST.update(i,i+1,enemy[i][1])

    count2 = 0
    for i in range(N):
        v = ST.query(i)
        if v>0:
            count2 += v
            j = bisect(i)
            ST.update(i,j+1,-v) 

    print(min(count1,count2))

if __name__ == '__main__':
    main()