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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

#!/usr/bin/ruby

require 'pp'

N,D,A  = gets.chomp.split(" ").map(&:to_i)

$monsters = []
1.upto(N){|i|
  x,h  = gets.chomp.split(" ").map(&:to_i)
  $monsters << [x,h]
}

$monsters.sort_by!{|e| e[0]}

def bomb(left, right, a)
  #puts "left=#{left}, right=#{right}"
  l = $monsters.bsearch_index{|x| x[0] >= left }
  r = $monsters.bsearch_index{|x| x[0] > right}

  if r == nil
    r = $monsters.size - 1
  else
    r -= 1 if l < r
  end

  if $monsters[l][1]%a == 0
    c = $monsters[l][1]/a
  else
    c = $monsters[l][1]/a + 1
  end

  # puts "l=#{l}, r=#{r}"

  l.upto(r){|i|
    $monsters[i][1] -= c * a
  }

  $monsters.select!{|e| e[1] > 0}

  return c
end


count = 0
while $monsters.size != 0
  #pp $monsters
  count += bomb($monsters[0][0], $monsters[0][0] + 2*D, A)

  #pp $monsters
end

puts count