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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

internal data class Enemy(
    var hp: Int
)

internal fun MutableMap<Int, Enemy>.leftAlive(): Pair<Int, Enemy>? {
    val alive = this.filter { it.value.hp > 0 }
    return if (alive.isEmpty()) {
        null
    } else {
        alive.toSortedMap().firstKey().let { Pair(it, this[it]!!) }
    }
}

internal fun MutableMap<Int, Enemy>.bomb(distance: IntRange, attack: Int) {
    this.filter { it.key in distance }.map { it.value.hp -= attack }
}

internal fun solve(
    enemies: MutableMap<Int, Enemy>,
    d: Int,
    a: Int
): Int {
    val orderedEnemies = enemies.toSortedMap()
    var count = 0
    while (true) {
        val left = orderedEnemies.leftAlive() ?: break
        val bombCount = if (left.second.hp % a == 0){
            left.second.hp / a
        } else{
            left.second.hp / a + 1
        }
        orderedEnemies.bomb(left.first..left.first + (d * 2), a * bombCount)
        count += bombCount
    }
    return count
}


fun main(args: Array<String>) {
    var OUTPUT = ""

    val br = System.`in`.bufferedReader()
    val (n, d, a) = br.readLine().split(" ").map { it.toInt() }
    val enemies = mutableMapOf<Int, Enemy>()
    repeat(n) { br.readLine().split(" ").map { it.toInt() }.let { enemies.put(it[0], Enemy(it[1])) } }

    OUTPUT += solve(enemies, d, a).toString()
    print(OUTPUT)
}