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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Windows;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    public class Program
    {
        private static long mod = 1000000007;

        static void Main(string[] args)
        {
            var r1 = ReadSplit();
            var n = r1[0].Int();
            var d = r1[1].Long();
            var a = r1[2].Long();
            var dic = new SortedDictionary<long, long>();
            for (int i = 0; i < n; i++)
            {
                var r2 = ReadSplit();
                var x = r2[0].Long();
                var h = r2[1].Long();
                dic.Add(x, h);
            }
            var last = dic.Last().Key;
            var left = d + dic.First().Key;
            var ans = 0L;
            while (true)
            {
                long h;
                dic.TryGetValue(left - d, out h);
                var count = h / a;
                if (h % a != 0)
                {
                    count++;
                }
                var tD = a * count;
                var tmpLeft = left;
                for (long j = left; j >= left - d; j--)
                {
                    long tmp;
                    if(dic.TryGetValue(j, out tmp))
                    {
                        dic[j] -= tD;
                        if (dic[j] <= 0)
                        {
                            dic[j] = 0;
                        }
                        else
                        {
                            tmpLeft = j + d;
                        }
                    }
                }
                for (long j = left + 1; j <= left + d; j++)
                {
                    long tmp;
                    if (dic.TryGetValue(j, out tmp))
                    {
                        dic[j] -= tD;
                        if (dic[j] <= 0)
                        {
                            dic[j] = 0;
                        }
                        else if (left == tmpLeft)
                        {
                            tmpLeft = j + d;
                        }
                    }
                }
                ans += count;
                if (left == tmpLeft)
                {
                    tmpLeft = dic.Where(x => x.Value > 0).FirstOrDefault().Key + d;
                }
                if (left == tmpLeft) break;
                left = tmpLeft;
            }
            WriteRead(ans);
        }

        public static string Read()
        {
            return Console.ReadLine();
        }

        public static string[] ReadSplit()
        {
            return Console.ReadLine().Split(' ');
        }

        public static void WriteRead(object str)
        {
            Console.WriteLine(str);
            Read();
        }

        public static void Write(object str)
        {
            Console.WriteLine(str);
        }

        private static bool ChangeMin<T>(ref T a, T b) where T : IComparable
        {
            if (a.CompareTo(b) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }

        private static bool ChangekMax<T>(ref T a, T b) where T : IComparable
        {
            if (b.CompareTo(a) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }
    }
}


public static class Extentions
{
    public static int Int(this object obj)
    {
        return int.Parse(obj.ToString());
    }

    public static long Long(this object obj)
    {
        return long.Parse(obj.ToString());
    }

    public static decimal Decimal(this object obj)
    {
        return decimal.Parse(obj.ToString());
    }

    public static double Double(this object obj)
    {
        return double.Parse(obj.ToString());
    }

    public static T2 GetValueZero<T1, T2>(this Dictionary<T1, T2> d, T1 key) where T2 : struct
    {
        T2 value;
        if (d.TryGetValue(key, out value))
        {
            return value;
        }
        return new T2();
    }
}