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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function main(input) {
  var N = input[0].split(" ")[0]-0;
  var D = input[0].split(" ")[1]-0;
  var A = input[0].split(" ")[2]-0;
  var list = [];
  for(var i=1;i<=N;i++){
    list.push(input[i].split(" ").map(v=>v-0));
  }
  list = list.sort((a,b)=>a[0]-b[0]);

  var ans = 0;
  for (var i = 0; i < N; i++) {
    var x = list[i];
    if(x[1] > 0){
      var time = Math.ceil(x[1]/A);
      ans += time;
      for(var j=i;j<N;j++){
        var y = list[j];
        if(y[0]<=x[0]+D*2+1){
          y[1] -= A*time;
        }else{
          break;
        }
      }
    }
  }
  console.log(ans);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8').split("\n"))