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 C (GCC 5.4.1) (judge verdict: Accepted)

#define _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <stdlib.h>

#define N_MAX (200000)

typedef struct {
  size_t X; /* モンのX座標 */
  size_t H; /* モンのHP */
} Monster;

static size_t N;                        /* モンの総数 */
static size_t D;                        /* 爆弾のレンジ */
static size_t A;                        /* 爆弾のダメージ */
static Monster M[N_MAX];                /* モン達 */
static size_t  L[N_MAX];                /* 巻き添え開始位置(詳細は後述) */
static unsigned long long Y[N_MAX + 1]; /* 累計ダメージ量 */

int cmp(const void* lhs, const void* rhs) {
  return ((const Monster*)lhs)->X - ((const Monster*)rhs)->X;
}

int main(void) {
  size_t i, j, c;
  static unsigned long long y, result = 0;
  /* 入力チェックは全て省略 */
  scanf(" %u %u %u", &N, &D, &A);
  for (i = 0; i < N; ++i) {
    scanf(" %u %u", &M[i].X, &M[i].H);
  }
  /* モンを左から順に並べ替えておく */
  qsort(M, N, sizeof(Monster), cmp);

  /* i番目のモンが巻き添えを受け始める位置を計算し、L[i]に格納する */
  /* ※O(N)で計算可能だから性能上がるんじゃないか、という主張 */
  j = 0;
  for (i = 0; i < N; ++i) {
    while ((j < i) && (M[j].X + 2 * D < M[i].X))
      ++j;
    L[i] = j;
  }

  /* 左のモンから順にムッコロス */
  /* ※最左のモンにCeiling(モンのHP/爆弾のダメージ)回 */
  /*   当てるのは必要経費なので */
  for (i = 0; i < N; ++i) {
    /* 以前にモンを倒したときの巻き添えダメージ量を計算 */
    y = Y[i] - Y[L[i]];
    /* 巻き添えで倒し切れていない場合のみ、残りHPを削る */
    if (y < M[i].H) {
      /* たぶんCeiling(モンの残りHP/爆弾のダメージ)になっているはず */
      c = (M[i].H - (size_t)y + A - 1) / A;
      /* 以降の巻き添え計算用に、累計ダメージ量を控えておく*/
      Y[i + 1] = Y[i] + c * (unsigned long long)A;
      /* 爆弾の総使用回数を計上 */
      result += c;
    }
    else {
      Y[i + 1] = Y[i];
    }
  }
  printf("%llu\n", result);
  return 0;
}