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、攻撃から差し引くポイント
ans=0
cnt=0

attack_point=0
for x,h in XH:
    while q:
        if x<q[0][0]:break
        end_x,end_point=q.popleft()
        attack_point-=end_point

    if h<=attack_point:
        pass
    else:
        if h%A==0:
            cnt=(h-attack_point)/A
        else:
            cnt=(h-attack_point)/A+1
        attack_point+=cnt*A
        q.append((x+2*D+1,cnt*A))
        ans+=cnt

print ans