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 PYTHON3):

Solution:
import sys
n,d,a=map(int,input().split())
xh=[]
xx=[]
for i in range(n):
    x,h=map(int,input().split())
    xx.append(x)
    xh.append((x,h//a+(h%a>0)))
xh.sort()
xx.sort()
dp=[0]*n
import bisect
buf=0
count=0
if d==0:
    for i in range(n):
        count+=xh[i][1]
    print(count)
    sys.exit()
for i in range(n):
    #print(buf)
    buf+=dp[i]
    y=max(xh[i][1]-buf,0)
    count+=y
    buf+=y
    idx=bisect.bisect_left(xx,xx[i]+2*d+1)
    if idx>=n:
        continue
    dp[idx]-=y
    #print(dp,y,buf)
print(count)