Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3 3 2
1 2
5 4
9 2

Sample Output 1

2

First, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.

Then, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.

Now, all the monsters' healths are 0.
We cannot make all the monsters' health drop to 0 or below with just one bomb.

Sample Input 2

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

Sample Output 2

5

We should use five bombs at the coordinate 5.

Sample Input 3

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000

Sample Output 3

3000000000

Watch out for overflow.

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

import sys, collections
input = sys.stdin.readline
N, D, A = [int(_) for _ in input().split()]
XH = sorted([[int(_) for _ in input().split()] for _ in range(N)])
R = collections.deque([])
bombs_ = {}
for i, xh in enumerate(XH):
    R += [xh[0] + 2 * D + 1]
    while R[0] <= xh[0]:
        bombs_[R.popleft() - 2 * D - 1] = i
while R:
    bombs_[R.popleft() - 2 * D - 1] = i + 1
bombs = {}
for i, xh in enumerate(XH):
    bombs[i] = bombs_[XH[i][0]]


class LazySegmentTree():
    def __init__(self, array, f, g, h, ti, ei):
        """
        Parameters
        ----------
        array : list
            to construct segment tree from
        f : func
            binary operation of the monoid
            T x T -> T
            T is dat
        g : func
            binary operation of the monoid
            T x E -> T
            T is dat, E is laz
        h : func
            binary operation of the monoid
            E x E -> T
            E is laz
        ti : T
            identity element of T
        ei : E
            identity element of E
        """
        self.f = f
        self.g = g
        self.h = h
        self.ti = ti
        self.ei = ei
        self.height = height = len(array).bit_length()
        self.n = n = 2**height
        self.dat = dat = [ti] * n + array + [ti] * (n - len(array))
        self.laz = [ei] * (2 * n)
        for i in range(n - 1, 0, -1):  # build
            dat[i] = f(dat[i << 1], dat[i << 1 | 1])

    def reflect(self, k):
        dat = self.dat
        ei = self.ei
        laz = self.laz
        g = self.g
        return self.dat[k] if laz[k] is ei else g(dat[k], laz[k])

    def evaluate(self, k):
        laz = self.laz
        ei = self.ei
        reflect = self.reflect
        dat = self.dat
        h = self.h
        if laz[k] is ei:
            return
        laz[(k << 1) | 0] = h(laz[(k << 1) | 0], laz[k])
        laz[(k << 1) | 1] = h(laz[(k << 1) | 1], laz[k])
        dat[k] = reflect(k)
        laz[k] = ei

    def thrust(self, k):
        height = self.height
        evaluate = self.evaluate
        for i in range(height, 0, -1):
            evaluate(k >> i)

    def recalc(self, k):
        dat = self.dat
        reflect = self.reflect
        f = self.f
        while k:
            k >>= 1
            dat[k] = f(reflect((k << 1) | 0), reflect((k << 1) | 1))

    def update(self, a, b, x):  # set value at position [a, b) (0-indexed)
        thrust = self.thrust
        n = self.n
        h = self.h
        laz = self.laz
        recalc = self.recalc
        a += n
        b += n - 1
        l = a
        r = b + 1
        thrust(a)
        thrust(b)
        while l < r:
            if l & 1:
                laz[l] = h(laz[l], x)
                l += 1
            if r & 1:
                r -= 1
                laz[r] = h(laz[r], x)
            l >>= 1
            r >>= 1
        recalc(a)
        recalc(b)

    def set_val(self, a, x):
        n = self.n
        thrust = self.thrust
        dat = self.dat
        laz = self.laz
        recalc = self.recalc
        ei = self.ei
        a += n
        thrust(a)
        dat[a] = x
        laz[a] = ei
        recalc(a)

    def get_val(self, a):
        a += self.n
        res = self.dat[a]
        while a:
            if self.laz[a] != self.ei:
                res = self.g(res, self.laz[a])
            a //= 2
        return res

    def query(self, a, b):  # result on interval [a, b) (0-indexed)
        f = self.f
        ti = self.ti
        n = self.n
        thrust = self.thrust
        reflect = self.reflect
        a += n
        b += n - 1
        thrust(a)
        thrust(b)
        l = a
        r = b + 1
        vl = vr = ti
        while l < r:
            if l & 1:
                vl = f(vl, reflect(l))
                l += 1
            if r & 1:
                r -= 1
                vr = f(reflect(r), vr)
            l >>= 1
            r >>= 1
        return f(vl, vr)


#RMQ and RAQ
array = [(xh[1], 1) for xh in XH]
f = max
g = lambda a, b: (a[0] + a[1] * b, a[1])
h = lambda a, b: a + b
ti = (-float('inf'), 0)
ei = 0

LST = LazySegmentTree(array=array, ti=ti, ei=ei, f=f, g=g, h=h)
ans = 0
for i in range(N):
    this = LST.query(i, i + 1)[0]
    if this > 0:
        c = (this - 1) // A + 1
        ans += c
        LST.update(i, bombs[i], -A * c)
print(ans)