Problem: 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.

Examples

Input

3 3 2
1 2
5 4
9 2


Output

2


Input

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5


Output

5


Input

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000


Output

3000000000

Solution (in PYTHON):

Solution:
# -*- coding: utf-8 -*-
import sys
from collections import deque

N,D,A=map(int, sys.stdin.readline().split())
XH=[ map(int, sys.stdin.readline().split()) for _ in range(N) ]
XH.sort()

q=deque()   #（攻撃が無効となる座標、攻撃によるポイント）
ans=0
cnt=0

attack_point=0
for x,h in XH:
    while q:
        if x<q[0][0]:break  #無効となる攻撃がない場合はwhileを終了
        end_x,end_point=q.popleft()
        attack_point-=end_point #攻撃が無効となる座標<=現在の座標があれば、その攻撃のポイントを引く

    if h<=attack_point: #モンスターの体力よりも攻撃で減らせるポイントの方が大きければ新規攻撃は不要
        pass
    else:   #新規攻撃が必要な場合
        if h%A==0:
            cnt=(h-attack_point)/A  #モンスターの大量をゼロ以下にするために何回攻撃が必要か
        else:
            cnt=(h-attack_point)/A+1
        attack_point+=cnt*A
        q.append((x+2*D+1,cnt*A))   #（攻撃が無効となる座標、攻撃によるポイント）をキューに入れる
        ans+=cnt

print ans