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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<vector<vector<ll>>> vvvll;
typedef vector<bool> vb;
typedef vector<vector<bool>> vvb;
typedef vector<vector<vector<bool>>> vvvb;
typedef pair<ll, ll> pll;
typedef vector<pll> vpll;
typedef vector<vpll> vvpll;
typedef vector<double> vd;
typedef vector<vd> vdd;

#define FOR(i,x,y) for(ll i=(ll)x; i<(ll)y; ++i)
#define REP(i,y) FOR(i, 0, y)
#define RFOR(i,x,y) for(ll i=(ll)x; i>=(ll)y; --i)
#define RREP(i,x) RFOR(i, x, 0)
#define ALL(a) a.begin(), a.end()
#define pb push_back
#define debug_print(x...) cerr << "line " << __LINE__ << " : "; debug_print_in(x);

template <typename First>
void debug_print_in(First first){
  cerr << first << endl;
  return;
}

template <typename First, typename... Rest>
void debug_print_in(First first, Rest... rest){
  cerr << first << " ";
  debug_print_in(rest...);
  return;
}

void IN(void){
  return;
}

template <typename First, typename... Rest>
void IN(First& first, Rest&... rest){
  cin >> first;
  IN(rest...);
  return;
}

template <typename First>
void OUT(First first){
  cout << first << endl;
  return;
}

template <typename First, typename... Rest>
void OUT(First first, Rest... rest){
  cout << first << " ";
  OUT(rest...);
  return;
}

template<class t, class u> void chmax(t&a,u b){if(a<b)a=b;};
template<class t, class u> void chmin(t&a,u b){if(a>b)a=b;};
int popcount(int t){return __builtin_popcount(t);} //GCC
int popcount(ll t){return __builtin_popcountll(t);} //GCC

template <typename T>
void vec_print(vector<T> VEC){
  REP(i, VEC.size()){
    cerr << VEC[i] << " ";
  }
  cerr << endl;
};

template <typename T>
void mat_print(vector<vector<T> > MAT){
  REP(i,MAT.size()){
    REP(j,MAT[i].size()){
      cerr << MAT[i][j] << " ";
    }
    cerr << endl;
  }
};

constexpr int INF = (1<<30);
constexpr ll INFLL = 1LL<<62;
constexpr long double EPS = 1e-12;
constexpr ll MOD = (ll)((1E+9)+7);

class Segment_Tree{
  private:
    ll n;
    ll n_;
    ll query_type;

  public:
    vector<ll> dat;
    vector<ll> lazy1; //遅延評価 - http://tsutaj.hatenablog.com/entry/2017/03/30/224339
    vector<ll> lazy2; //遅延評価 - http://tsutaj.hatenablog.com/entry/2017/03/30/224339
    vector<bool> lazy1_flag;
    vector<bool> lazy2_flag;
    Segment_Tree(ll n__, ll query_type_=0){
      // For simply, the number of component is set to be power of 2
      // query_type = 0 : min
      // query_type = 1 : max
      // query_type = 2 : sum
      n = 1;
      n_ = n__;
      while(n < n_) n*=2;

      query_type = query_type_;

      lazy1.resize(2*n-1, 0);
      lazy1_flag.resize(2*n-1, false);
      if(query_type==0){
        dat.resize(2*n-1, INFLL);
        lazy2.resize(2*n-1, INFLL);
      }else if(query_type==1){
        dat.resize(2*n-1, -(INFLL-1));
        lazy2.resize(2*n-1, -(INFLL-1));
      }else if(query_type==2){
        dat.resize(2*n-1, 0);
        lazy2.resize(2*n-1, 0);
      }
      lazy2_flag.resize(2*n-1, false);
      return;
    };

    ~Segment_Tree(void){
      return;
    };

    void eval1(ll k, ll l, ll r){
      if(lazy1_flag[k]){
        dat[k] = lazy1[k];

        if(r-l>1){
          if(query_type==0){
            lazy1[2*k+1] = lazy1[k];
            lazy1[2*k+2] = lazy1[k];
          }else if(query_type==1){
            lazy1[2*k+1] = lazy1[k];
            lazy1[2*k+2] = lazy1[k];
          }else if(query_type==2){
            lazy1[2*k+1] = lazy1[k]/2;
            lazy1[2*k+2] = lazy1[k]/2;
          }
        }
        lazy1_flag[2*k+1] = true;
        lazy1_flag[2*k+2] = true;

        lazy1_flag[k] = false;
        if(query_type==0)
          lazy1[k] = INFLL;
        else if(query_type==1)
          lazy1[k] = -(INFLL-1);
        else if(query_type==2)
          lazy1[k] = 0;
      }
    }

    void eval2(ll k, ll l, ll r){
      if(lazy2_flag[k]){
        if(query_type==0)
          dat[k] = min(dat[k], lazy2[k]);
        else if(query_type==1)
          dat[k] = max(dat[k], lazy2[k]);
        else if(query_type==2)
          dat[k] = dat[k]+lazy2[k];

        if(r-l>1){
          if(query_type==0){
            lazy2[2*k+1] = min(lazy2[2*k+1], lazy2[k]);
            lazy2[2*k+2] = min(lazy2[2*k+2], lazy2[k]);
          }else if(query_type==1){
            lazy2[2*k+1] = max(lazy2[2*k+1], lazy2[k]);
            lazy2[2*k+2] = max(lazy2[2*k+2], lazy2[k]);
          }else if(query_type==2){
            lazy2[2*k+1] += lazy2[k] / 2;
            lazy2[2*k+2] += lazy2[k] / 2;
          }
          lazy2_flag[2*k+1] = true;
          lazy2_flag[2*k+2] = true;
        }

        lazy2_flag[k] = false;
        if(query_type==0)
          lazy2[k] = INFLL;
        else if(query_type==1)
          lazy2[k] = -(INFLL-1);
        else if(query_type==2)
          lazy2[k] = 0;
      }
    }

    //k-th value is changed to a
    void update1(ll k, ll a){
      k += n-1;
      dat[k] = a;
      while(k>0){
        k = (k-1)/2;
        if(query_type==0)
          dat[k] = min(dat[k*2+1], dat[k*2+2]);
        else if(query_type==1)
          dat[k] = max(dat[k*2+1], dat[k*2+2]);
        else if(query_type==2)
          dat[k] = dat[k*2+1]+dat[k*2+2];
      }
      return;
    };

    //k-th value is operated of a
    void update2(ll k, ll a){
      k += n-1;
      if(query_type==0)
        dat[k] = min(dat[k], a);
      else if(query_type==1)
        dat[k] = max(dat[k], a);
      else if(query_type==2)
        dat[k] = dat[k]+a;
      while(k>0){
        k = (k-1)/2;
        if(query_type==0)
          dat[k] = min(dat[k*2+1], dat[k*2+2]);
        else if(query_type==1)
          dat[k] = max(dat[k*2+1], dat[k*2+2]);
        else if(query_type==2)
          dat[k] = dat[k*2+1]+dat[k*2+2];
      }
      return;
    };

    //[a,b)の範囲の値をxに変える
    void rangeupdate1(ll a, ll b, ll x, ll k=0, ll l=0, ll r=-1){
      if(r<0) r=n;

      eval1(k,l,r);

      if(r<=a || b<=l){
        return;
      }

      if(a<=l && r<=b){
        if(query_type==0)
          lazy1[k] = x;
        else if(query_type==1)
          lazy1[k] = x;
        else if(query_type==2)
          lazy1[k] = (r-l)*x;
        lazy1_flag[k] = true;
        eval1(k,l,r);
      }else{
        rangeupdate1(a, b, x, 2*k+1, l, (l+r)/2);
        rangeupdate1(a, b, x, 2*k+2, (l+r)/2, r);
        if(query_type==0)
          dat[k] = min(dat[2*k+1], dat[2*k+2]);
        else if(query_type==1)
          dat[k] = max(dat[2*k+1], dat[2*k+2]);
        else if(query_type==2)
          dat[k] = dat[2*k+1] + dat[2*k+2];
      }
      return;
    }

    //[a,b)の範囲に対してxを作用させる
    void rangeupdate2(ll a, ll b, ll x, ll k=0, ll l=0, ll r=-1){
      if(r<0) r=n;

      eval2(k,l,r);

      if(r<=a || b<=l){
        return;
      }

      if(a<=l && r<=b){
        if(query_type==0)
          lazy2[k] = min(lazy2[k], x);
        if(query_type==1)
          lazy2[k] = max(lazy2[k], x);
        if(query_type==2)
          lazy2[k] = lazy2[k] + (r-l)*x;
        lazy2_flag[k] = true;
        eval2(k,l,r);
      }else{
        rangeupdate2(a, b, x, 2*k+1, l, (l+r)/2);
        rangeupdate2(a, b, x, 2*k+2, (l+r)/2, r);
        if(query_type==0)
          dat[k] = min(dat[2*k+1], dat[2*k+2]);
        else if(query_type==1)
          dat[k] = max(dat[2*k+1], dat[2*k+2]);
        else if(query_type==2)
          dat[k] = dat[2*k+1] + dat[2*k+2];
      }
      return;
    }

    // search the minimum of [a, b)
    // Other values are used for simply
    // From outside, call query(a, b, 0, 0, n)
    // k is the node index, 
    // temporary block is [l, r)
    ll query(ll a, ll b, ll k, ll l, ll r){
      //if there are no overlap between [a, b) and [l, r)
      if(r<=a || b<=l){
        if(query_type==0)
          return INFLL;
        else if(query_type==1)
          return -(INFLL-1);
        else if(query_type==2)
          return 0;
      }

      eval1(k,l,r);
      eval2(k,l,r);

      //if [a, b) contains [l, r), return the value of this node
      if(a<=l && r<=b) return dat[k];

      ll vl = query(a, b, k*2+1, l, (l+r)/2);
      ll vr = query(a, b, k*2+2, (l+r)/2, r);
      if(query_type==0)
        return min(vl, vr);
      else if(query_type==1)
        return max(vl, vr);
      else if(query_type==2)
        return vl+vr;
    };

    // search the minimum of [a, b)
    ll query(ll a, ll b){
      if(a<0 || n_<b || a==b){
        fprintf(stderr, "Segment_Tree Search Space Error\n");
        fprintf(stderr, "Desired:\n");
        fprintf(stderr, "%lld <= %lld < %lld <= %lld\n", 0, a, b, n_);
        exit(0);
      }
      return query(a, b, 0, 0, n);
    };
};

int main(){
  cin.tie(0); // cut the cin and cout (default, std::flush is performed after std::cin)
  ios::sync_with_stdio(false); // cut the iostream and stdio (DON'T endl; BUT "\n";)

  ll N, D, A;
  IN(N, D, A);
  vpll XH(N);
  REP(i,N) IN(XH[i].first, XH[i].second);
  sort(ALL(XH));

  Segment_Tree que(N, 2);
  REP(i,N){
    que.update1(i,XH[i].second);
  }

  vll R(N, N);
  ll head = 0;
  REP(i, N){
    if(head>=N) break;
    while(XH[head].first-XH[i].first<=2*D){
      head++;
      if(head>=N) break;
    }
    R[i] = head;
    //fprintf(stderr, "%lld %lld\n", i, head);
  }

  /*
  fprintf(stderr, "R:\n");
  REP(i,N){
    fprintf(stderr, "%lld : %lld\n", i, R[i]);
  }
  fprintf(stderr, "\n");
  */
  
  ll first=0;
  ll ans = 0;
  while(first<N){
    ll H_tmp = que.query(first, first+1);
    ll ans_tmp = H_tmp/A;
    //fprintf(stderr, "%lld %lld\n", first, ans_tmp);
    if(ans_tmp*A!=H_tmp) ans_tmp++;
    ans += ans_tmp;
    //fprintf(stderr, "%lld %lld\n", first, ans_tmp);
    /*
    REP(i,N){
      fprintf(stderr, "%lld: %lld\n", i, que.query(i, i+1));
    }
    */
    que.rangeupdate2(first,R[first],-ans_tmp*A);
    while(que.query(first, first+1)<=0){
      //fprintf(stderr, "%lld %lld\n", first, que.query(first, first+1));
      first++;
      if(first>=N) break;
    }
  }

  OUT(ans);




  return 0;
}