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 Rust (1.15.1) (judge verdict: Accepted)

// The main code is at the very bottom.

#[allow(unused_imports)]
#[macro_use]
pub mod spella {
  pub mod byte {
    pub use self::byte_char::*;
    pub use self::byte_str::*;
    pub use self::byte_string::*;
    pub use self::from_byte_str::*;

    mod byte_char {
      use std::fmt::{self, Debug, Display, Formatter};

      #[derive(Clone, Copy, Default, PartialEq, Eq, PartialOrd, Ord, Hash)]
      pub struct ByteChar(pub u8);

      impl Debug for ByteChar {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          write!(f, "b'{}'", self.0 as char)
        }
      }

      impl Display for ByteChar {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          write!(f, "{}", self.0 as char)
        }
      }
    }

    mod byte_str {
      use spella::byte::{ByteChar, ByteString};
      use std::fmt::{self, Debug, Display, Formatter};
      use std::ops::{Deref, DerefMut};

      #[derive(PartialEq, Eq, PartialOrd, Ord, Hash)]
      pub struct ByteStr([ByteChar]);

      macro_rules! cast {
        (mut $x:expr, $($T:ty)=>*) => {
          unsafe { &mut *($x $(as *mut $T)*) }
        };
        ($x:expr, $($T:ty)=>*) => {
          unsafe { &*($x $(as *const $T)*) }
        };
      }

      impl ByteStr {
        pub fn from_bytes(s: &[u8]) -> &Self {
          cast!(s, [u8] => [ByteChar] => ByteStr)
        }

        pub fn from_bytes_mut(s: &mut [u8]) -> &mut Self {
          cast!(mut s, [u8] => [ByteChar] => ByteStr)
        }

        pub fn from_byte_chars(s: &[ByteChar]) -> &Self {
          cast!(s, [ByteChar] => ByteStr)
        }

        pub fn from_byte_chars_mut(s: &mut [ByteChar]) -> &mut Self {
          cast!(mut s, [ByteChar] => ByteStr)
        }

        pub fn as_byte_chars(&self) -> &[ByteChar] {
          &self.0
        }

        pub fn as_byte_chars_mut(&mut self) -> &mut [ByteChar] {
          &mut self.0
        }

        pub fn as_bytes(&self) -> &[u8] {
          cast!(self, ByteStr => [ByteChar] => [u8])
        }

        pub fn as_bytes_mut(&mut self) -> &mut [u8] {
          cast!(mut self, ByteStr => [ByteChar] => [u8])
        }
      }

      impl ToOwned for ByteStr {
        type Owned = ByteString;

        fn to_owned(&self) -> ByteString {
          ByteString::from(self.0.to_owned())
        }
      }

      impl Debug for ByteStr {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          write!(f, "b\"")?;

          for &c in &self.0 {
            write!(f, "{}", c)?;
          }

          write!(f, "\"")
        }
      }

      impl Display for ByteStr {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          for &c in &self.0 {
            write!(f, "{}", c)?;
          }

          Ok(())
        }
      }

      impl Deref for ByteStr {
        type Target = [ByteChar];

        fn deref(&self) -> &[ByteChar] {
          self.as_byte_chars()
        }
      }

      impl DerefMut for ByteStr {
        fn deref_mut(&mut self) -> &mut [ByteChar] {
          self.as_byte_chars_mut()
        }
      }
    }

    mod byte_string {
      use spella::byte::{ByteChar, ByteStr};

      use std::borrow::{Borrow, BorrowMut};
      use std::fmt::{self, Debug, Display, Formatter};
      use std::ops::{Deref, DerefMut};

      #[derive(Clone, Default, PartialEq, Eq, PartialOrd, Ord, Hash)]
      pub struct ByteString(Vec<ByteChar>);

      impl ByteString {
        pub fn into_byte_chars(self) -> Vec<ByteChar> {
          self.0
        }

        pub fn as_byte_str(&self) -> &ByteStr {
          ByteStr::from_byte_chars(&self.0)
        }

        pub fn as_mut_byte_str(&mut self) -> &mut ByteStr {
          ByteStr::from_byte_chars_mut(&mut self.0)
        }
      }

      impl From<Vec<ByteChar>> for ByteString {
        fn from(s: Vec<ByteChar>) -> ByteString {
          ByteString(s)
        }
      }

      impl Borrow<ByteStr> for ByteString {
        fn borrow(&self) -> &ByteStr {
          self.as_byte_str()
        }
      }

      impl BorrowMut<ByteStr> for ByteString {
        fn borrow_mut(&mut self) -> &mut ByteStr {
          self.as_mut_byte_str()
        }
      }

      impl Debug for ByteString {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          Debug::fmt(self.as_byte_str(), f)
        }
      }

      impl Display for ByteString {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          Display::fmt(self.as_byte_str(), f)
        }
      }

      impl Deref for ByteString {
        type Target = ByteStr;

        fn deref(&self) -> &ByteStr {
          ByteStr::from_byte_chars(&self.0)
        }
      }

      impl DerefMut for ByteString {
        fn deref_mut(&mut self) -> &mut ByteStr {
          ByteStr::from_byte_chars_mut(&mut self.0)
        }
      }
    }

    mod from_byte_str {
      use spella::byte::{ByteChar, ByteStr, ByteString};

      use std::error::Error;
      use std::fmt::{self, Debug, Display, Formatter};
      use std::str::{self, FromStr, Utf8Error};

      pub trait FromByteStr: Sized {
        type Err;

        fn from_byte_str(s: &ByteStr) -> Result<Self, Self::Err>;
      }

      macro_rules! fn_description {
        () => {
          fn description(&self) -> &str {
            "description() is deprecated; use Display"
          }
        };
      }

      #[derive(Debug)]
      pub struct ParseByteCharError(ParseByteCharErrorKind);

      #[derive(Debug)]
      enum ParseByteCharErrorKind {
        EmptyByteStr,
        TooManyByteChars,
      }

      impl Display for ParseByteCharError {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          use self::ParseByteCharErrorKind::*;

          f.write_str(match self.0 {
            EmptyByteStr => "empty `ByteStr`",
            TooManyByteChars => "too many `ByteChar`s",
          })
        }
      }

      impl Error for ParseByteCharError {
        fn_description! {}
      }

      impl FromByteStr for ByteChar {
        type Err = ParseByteCharError;

        fn from_byte_str(s: &ByteStr) -> Result<Self, Self::Err> {
          use self::ParseByteCharErrorKind::*;

          match s.len() {
            1 => Ok(unsafe { *s.get_unchecked(0) }),
            0 => Err(ParseByteCharError(EmptyByteStr)),
            _ => Err(ParseByteCharError(TooManyByteChars)),
          }
        }
      }

      #[derive(Debug)]
      pub enum ParseByteStringError {}

      impl Display for ParseByteStringError {
        fn fmt(&self, _: &mut Formatter) -> fmt::Result {
          match *self {}
        }
      }

      impl Error for ParseByteStringError {
        fn_description! {}
      }

      impl FromByteStr for ByteString {
        type Err = ParseByteStringError;

        fn from_byte_str(s: &ByteStr) -> Result<Self, Self::Err> {
          Ok(ByteString::from(s.to_vec()))
        }
      }

      pub struct ParseFromStrError<T: FromStr>(ParseFromStrErrorKind<T>);

      enum ParseFromStrErrorKind<T: FromStr> {
        Utf8Error(Utf8Error),
        FromStrError(T::Err),
      }

      impl<T: FromStr> Debug for ParseFromStrError<T>
      where
        T::Err: Debug,
      {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          use self::ParseFromStrErrorKind::*;

          match self.0 {
            Utf8Error(ref err) => f.debug_tuple("Utf8Error").field(err).finish(),
            FromStrError(ref err) => f.debug_tuple("FromStrError").field(err).finish(),
          }
        }
      }

      impl<T: FromStr> Display for ParseFromStrError<T>
      where
        T::Err: Display,
      {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          use self::ParseFromStrErrorKind::*;

          match self.0 {
            Utf8Error(ref err) => write!(f, "{}", err),
            FromStrError(ref err) => write!(f, "{}", err),
          }
        }
      }

      impl<T: FromStr> Error for ParseFromStrError<T>
      where
        T::Err: Debug + Display,
      {
        fn_description! {}
      }

      impl<T: FromStr> FromByteStr for T {
        type Err = ParseFromStrError<T>;

        fn from_byte_str(s: &ByteStr) -> Result<T, Self::Err> {
          use self::ParseFromStrErrorKind::*;

          str::from_utf8(s.as_bytes())
            .map_err(|e| ParseFromStrError(Utf8Error(e)))
            .and_then(|s| s.parse().map_err(|e| ParseFromStrError(FromStrError(e))))
        }
      }
    }
  }

  pub mod io {
    pub use self::scanner::*;

    mod scanner {
      use spella::byte::{ByteStr, FromByteStr};

      use std::io::{self, BufRead};

      #[derive(Debug)]
      pub struct Scanner<R> {
        reader: R,
        buf: Vec<u8>,
        pos: usize,
      }

      const INITIAL_CAPACITY: usize = 32;

      impl<R: BufRead> Scanner<R> {
        pub fn new(reader: R) -> Self {
          Scanner {
            reader: reader,
            buf: Vec::with_capacity(INITIAL_CAPACITY),
            pos: 0,
          }
        }

        pub fn next<T: FromByteStr>(&mut self) -> io::Result<Result<T, T::Err>> {
          self.next_byte_str().map(T::from_byte_str)
        }

        pub fn next_byte_str(&mut self) -> io::Result<&ByteStr> {
          if self.buf.is_empty() {
            self.read_line()?;
          }

          loop {
            match self.buf.get(self.pos) {
              Some(&b' ') => self.pos += 1,
              Some(&b'\n') => self.read_line()?,
              Some(_) => break,
              None => return Err(io::Error::from(io::ErrorKind::UnexpectedEof)),
            }
          }

          let start = self.pos;
          self.pos += 1;

          loop {
            match self.buf.get(self.pos) {
              Some(&b' ') | Some(&b'\n') | None => break,
              Some(_) => self.pos += 1,
            }
          }

          Ok(ByteStr::from_bytes(&self.buf[start..self.pos]))
        }

        fn read_line(&mut self) -> io::Result<()> {
          self.buf.clear();
          self.pos = 0;
          self.reader.read_until(b'\n', &mut self.buf)?;

          Ok(())
        }
      }
    }
  }
}

#[allow(unused_imports)]
// https://github.com/niuez/rust-data-structures/tree/24bbb9324c57bf25262f8425498a02407ca92884
pub mod rust_data_structures {
  pub mod algebra {
    pub trait Magma: Sized + Clone {
      fn op(&self, rhs: &Self) -> Self;
    }

    pub trait Associative: Magma {}

    pub trait Unital: Magma {
      fn identity() -> Self;
    }

    pub trait Monoid: Magma + Associative + Unital {}

    impl<T: Magma + Associative + Unital> Monoid for T {}

    pub trait Effector: Monoid {
      type Target;
      fn effect(&self, t: &Self::Target, sz: usize) -> Self::Target;
    }
  }

  pub mod segment_tree {
    use super::algebra::*;

    pub struct LazySegmentTree<T: Monoid, E: Effector<Target = T>> {
      node: Vec<T>,
      lazy: Vec<E>,
      sz: usize,
    }

    impl<T: Monoid, E: Effector<Target = T>> LazySegmentTree<T, E> {
      pub fn init(vec: Vec<T>) -> Self {
        let mut sz = 1;
        while sz < vec.len() {
          sz *= 2
        }
        let mut node = vec![T::identity(); sz << 1];
        let lazy = vec![E::identity(); sz << 1];
        for i in 0..vec.len() {
          node[i + sz] = vec[i].clone();
        }
        for i in (1..sz).rev() {
          node[i] = node[i << 1].op(&node[(i << 1) + 1]);
        }
        LazySegmentTree {
          node: node,
          lazy: lazy,
          sz: sz,
        }
      }

      fn push(&mut self, i: usize, sz: usize) {
        self.node[i] = self.lazy[i].effect(&self.node[i], sz);
        if (i << 1) < self.node.len() {
          self.lazy[i << 1] = self.lazy[i << 1].op(&self.lazy[i]);
          self.lazy[(i << 1) + 1] = self.lazy[(i << 1) + 1].op(&self.lazy[i]);
        }
        self.lazy[i] = E::identity();
      }

      fn update_raw(&mut self, i: usize, a: usize, b: usize, l: usize, r: usize, e: &E) {
        self.push(i, r - l);
        if b <= l || r <= a {
          return;
        } else if a <= l && r <= b {
          self.lazy[i] = self.lazy[i].op(e);
          self.push(i, r - l);
        } else {
          self.update_raw(i << 1, a, b, l, (l + r) >> 1, e);
          self.update_raw((i << 1) + 1, a, b, (l + r) >> 1, r, e);
          self.node[i] = self.node[i << 1].op(&self.node[(i << 1) + 1]);
        }
      }

      pub fn update_range(&mut self, l: usize, r: usize, e: E) {
        let sz = self.sz;
        self.update_raw(1, l, r, 0, sz, &e);
      }

      fn fold_raw(&mut self, i: usize, a: usize, b: usize, l: usize, r: usize) -> T {
        self.push(i, r - l);
        if b <= l || r <= a {
          T::identity()
        } else if a <= l && r <= b {
          self.node[i].clone()
        } else {
          self
            .fold_raw(i << 1, a, b, l, (l + r) >> 1)
            .op(&self.fold_raw((i << 1) + 1, a, b, (l + r) >> 1, r))
        }
      }

      pub fn fold(&mut self, l: usize, r: usize) -> T {
        let sz = self.sz;
        self.fold_raw(1, l, r, 0, sz)
      }
    }
  }
}

mod prelude {
  pub use spella::byte::{ByteChar, ByteStr, ByteString};
  pub use std::collections::*;
  pub use std::io::prelude::*;
  pub use std::iter::FromIterator;
  pub use std::marker::PhantomData;
  pub use std::num::Wrapping;
  pub use std::ops::{Range, RangeFrom, RangeTo};
  pub use std::{cell, cmp, f64, i32, i64, isize, iter, mem, rc, str, time, u32, u64, usize};
}

use prelude::*;

const CUSTOM_STACK_SIZE_MEBIBYTES: Option<usize> = None;

fn main() {
  fn exec_solver() {
    let stdin = std::io::stdin();
    let stdout = std::io::stdout();
    #[cfg(not(debug_assertions))]
    let mut writer = std::io::BufWriter::new(stdout.lock());
    #[cfg(debug_assertions)]
    let mut writer = stdout.lock();
    solve(stdin.lock(), &mut writer);
    writer.flush().unwrap();
  }

  if let Some(stack_size_mebibytes) = CUSTOM_STACK_SIZE_MEBIBYTES {
    std::thread::Builder::new()
      .name("exec_solver".to_owned())
      .stack_size(stack_size_mebibytes * 1024 * 1024)
      .spawn(exec_solver)
      .unwrap()
      .join()
      .unwrap();
  } else {
    exec_solver();
  }
}

fn solve<R: BufRead, W: Write>(reader: R, mut writer: W) {
  let mut _scanner = spella::io::Scanner::new(reader);

  #[allow(unused_macros)]
  macro_rules! scan {
    ($T:ty) => {
      _scanner.next::<$T>().unwrap().unwrap()
    };
    ($($T:ty),+) => {
      ($(scan!($T)),+)
    };
    ($($T:ty),+; $n:expr $(; $m:expr)*) => {{
      (0..$n).map(|_| scan!($($T),+ $(; $m)*)).collect::<Vec<_>>()
    }};
  }

  #[allow(unused_macros)]
  macro_rules! scan_iter {
    ($($T:ty),+; $n:expr) => {
      (0..$n).map(|_| scan!($($T),+))
    };
  }

  #[allow(unused_macros)]
  macro_rules! print {
    ($fmt:expr) => {
      write!(writer, $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      write!(writer, $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! println {
    ($fmt:expr) => {
      writeln!(writer, $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      writeln!(writer, $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! eprint {
    ($fmt:expr) => {
      #[cfg(debug_assertions)]
      write!(std::io::stderr(), $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      #[cfg(debug_assertions)]
      write!(std::io::stderr(), $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! eprintln {
    ($fmt:expr) => {
      #[cfg(debug_assertions)]
      writeln!(std::io::stderr(), $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      #[cfg(debug_assertions)]
      writeln!(std::io::stderr(), $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! dbg {
    ($($x:expr),+) => {{
      eprintln!(concat!("[{}:{}] ", $(stringify!($x), " = {:?}; "),+), file!(), line!(), $($x),+);
    }};
  }

  use rust_data_structures::algebra::*;
  use rust_data_structures::segment_tree::*;

  #[derive(Clone, Debug)]
  struct Sm(i64);

  impl Magma for Sm {
    fn op(&self, right: &Self) -> Self {
      Sm(self.0 + right.0)
    }
  }
  impl Associative for Sm {}
  impl Unital for Sm {
    fn identity() -> Self {
      Sm(0)
    }
  }

  #[derive(Clone, Debug)]
  struct Aq(i64);

  impl Magma for Aq {
    fn op(&self, right: &Self) -> Self {
      Aq(self.0 + right.0)
    }
  }
  impl Associative for Aq {}
  impl Unital for Aq {
    fn identity() -> Self {
      Aq(0)
    }
  }
  impl Effector for Aq {
    type Target = Sm;
    fn effect(&self, t: &Self::Target, s: usize) -> Self::Target {
      Sm(t.0 + self.0 * s as i64)
    }
  }

  fn div_ceil(x: i64, y: i64) -> i64 {
    x / y + if x % y != 0 { 1 } else { 0 }
  }

  let (n, d, a) = scan!(usize, u64, i64);
  let mut xh = scan!(u64, i64; n);
  xh.sort();
  let xh = xh;

  let mut h = LazySegmentTree::init(xh.iter().map(|&(_, h_i)| Sm(h_i)).collect());
  let mut cnt = 0;
  for i in 0..n {
    if h.fold(i, i + 1).0 <= 0 {
      continue;
    }
    let t = div_ceil(h.fold(i, i + 1).0, a);
    cnt += t;
    let m = {
      let mut ok = i;
      let mut ng = n;
      while ng - ok > 1 {
        let mid = (ng + ok) / 2;
        if xh[mid].0 <= xh[i].0 + d * 2 {
          ok = mid;
        } else {
          ng = mid;
        }
      }
      ok + 1
    };
    h.update_range(i, m, Aq(-a * t));
  }
  println!("{}", cnt);
}