silver_Bovine_Acrobatics (USACO December_Contest)
Time limit: 2 seconds | Memory limit: 256 MB | Task type: batch
Algorithms: data structures, greedy

Farmer John has decided to make his cows do some acrobatics! First,  FJ weighs
his cows and finds that they have $N$ ($1\le N\le 2\cdot 10^5$) distinct
weights. In particular, for each $i\in [1,N]$, $a_i$ of his cows have a weight
of $w_i$
($1\le a_i\le 10^9, 1\le w_i\le 10^9$).
His most popular stunt involves the cows forming
balanced towers
. A
tower
is a sequence of cows where each cow is stacked on top of the next.
A tower is
balanced
if every cow with a cow directly above it has weight
at least $K$ ($1\le K\le 10^9$) greater than the weight of the cow directly
above it. Any cow can be part of at most one balanced tower.
If FJ wants to create at most $M$ ($1 \le M \le 10^9$) balanced towers of cows, at most
how many cows can be part of some tower?
INPUT FORMAT (input arrives from the terminal / stdin):
The first line contains three space-separated integers, $N$, $M$, and $K$.
The next $N$ lines contain two space-separated integers, $w_{i}$ and $a_i$. It
is guaranteed that all $w_i$ are distinct.
OUTPUT FORMAT (print output to the terminal / stdout):
Output the maximum number of cows in balanced towers if FJ helps the cows form towers
optimally.
SAMPLE INPUT:
3 5 2
9 4
7 6
5 5
SAMPLE OUTPUT:
14
FJ can create four balanced towers with cows of weights 5, 7, and 9, and one balanced tower with
cows of weights 5 and 7.
SAMPLE INPUT:
3 5 3
5 5
7 6
9 4
SAMPLE OUTPUT:
9
FJ can create four balanced towers with cows of weights 5 and 9, and one balanced tower with a cow
of weight 7. Alternatively, he can create four balanced towers with cows of weights 5 and
9, and one balanced tower with a cow of weight 5.
SCORING:
In inputs 3-5, $M \leq 5000$ and the total number of cows does not exceed
$5000$.
In inputs 6-11, the total number of cows does not exceed $2\cdot 10^5$.
Inputs 12-17 have no additional constraints.
Problem credits: Eric Hsu

Starter code:

Grader code:

Setup script:

Evaluation script: