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: Wrong Answer)

N, D, A = gets.split.map(&:to_i)
E = N.times.map { gets.split.map(&:to_i) }

E.sort_by! { |x, h| x }
ans = 0

dp = []

E.each do |x, h|
  if dp.empty?
    point = x + 2 * D
    cnt = Rational(h, A).ceil
    damage = A * cnt
    ans += cnt

    dp << [point, damage]
  else
    while !dp.empty? && dp[0][0] < x
      dp.shift
    end

    if dp.empty?
      point = x + 2 * D
      cnt = Rational(h, A).ceil
      damage = A * cnt
      ans += cnt

      dp << [point, damage]
    else
      po, damage = dp[0]
      remain = h - damage
      cnt = Rational(remain, A).ceil
      ans += cnt
      ad = A * cnt
      np = x + 2 * D
      dp[0][1] = damage + ad
      dp << [np, ad]
    end
  end
end

puts ans