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
# Date: 2020-01-08
# Author: lee215

import heapq
get = lambda: int(raw_input().strip())
getl = lambda: raw_input().strip()
gets = lambda: map(int, raw_input().strip().split())
getss = lambda n: [gets() for _ in xrange(n)]


N, D, A = gets()
XH = sorted(getss(N))

bombs = []
res = cur_b = 0
for x, h in XH:
    while bombs and bombs[0][0] < x - D:
        bx, bn = heapq.heappop(bombs)
        cur_b -= bn
    h -= cur_b * A
    if h <= 0: continue
    bn = (h + A - 1) / A if A > 1 else h
    cur_b += bn
    res += bn
    heapq.heappush(bombs, [x + D, bn])
print res