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:
N,D,A=map(int,input().split())
XH=[]
inf=float("inf")
for i in range(N):
    X,H=map(int,input().split())
    if H%A==0:
        H//=A
    else:
        H=H//A+1
    XH.append([X,H])
XH.sort()
XH=[[-inf,0]]+XH

L=0
lst=[0]*(N+1)
S=[0]*(N+1)
lst[1]=XH[1][1]
S[1]=lst[1]

for R in range(2,N+1):
    r=XH[R][0]
    l=r-2*D
    while XH[L][0]<l:
        L+=1
    lst[R]=max(0,XH[R][1]-(S[R-1]-S[L-1]))
    S[R]=lst[R]+S[R-1]
    
print(S[-1])