Bovine Acrobatics

문제

Farmer John has decided to make his cows do some acrobatics! First, FJ weighs his cows and finds that they have $NN$ ($1\le N\le 2\cdot {10}^{5}1\backslash le\; N\backslash le\; 2\backslash cdot\; 10^5$) distinct weights. In particular, for each $i\in [1,N]i\backslash in\; [1,N]$, $a_{i}a\_i$ of his cows have a weight of $w_{i}w\_i$ ($1\le a_i\le {10}^9,1\le w_i\le {10}^{9}1\backslash le\; a\_i\backslash le\; 10^9,\; 1\backslash le\; w\_i\backslash le\; 10^9$).

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 $KK$ ($1\le K\le {10}^{9}1\backslash le\; K\backslash le\; 10^9$) 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 $MM$ ($1\le M\le {10}^{9}1\; \backslash le\; M\; \backslash le\; 10^9$) balanced towers of cows, at most how many cows can be part of some tower?

입력

The first line contains three space-separated integers, $NN$, $MM$, and $KK$.

The next $NN$ lines contain two space-separated integers, $w_{i}w\_\{i\}$ and $a_{i}a\_i$. It is guaranteed that all $w_{i}w\_i$ are distinct.

출력

Output the maximum number of cows in balanced towers if FJ helps the cows form towers optimally.