Streaming Channels

Seolgwak is in charge of streaming a large conference. The conference has $N$ sessions, and session $i$ is held during the time interval $[S_i,E_i]$.

Seolgwak can use two streaming channels A and B. Channel A may stream for at most $L_A$ time units, and channel B may stream for at most $L_B$ time units. The streaming interval of channel A is chosen as $[a_A,b_A]$, where $a_A,b_A$ are nonnegative integer times, $0 \leq a_A \leq b_A$, and $b_A-a_A \leq L_A$. Channel B is chosen in the same way as $[a_B,b_B]$, with $0 \leq a_B \leq b_B$ and $b_B-a_B \leq L_B$.

The two channels cannot be operated at the same time. Formally, either $b_A \leq a_B$ or $b_B \leq a_A$ must hold. If one interval ends exactly when the other starts, this is not considered simultaneous operation.

A session $i$ is fully streamed if $[S_i,E_i]$ is completely contained in the streaming interval of channel A or channel B.

Choose the two streaming intervals to maximize the number of fully streamed sessions.

The input is given in the following format.

$N$ $L_A\ L_B$ $S_1\ E_1$ $S_2\ E_2$ $\vdots$ $S_N\ E_N$

Print the maximum possible number of fully streamed sessions.

• $1 \leq N \leq 200\ 000$.
• $1 \leq L_A,L_B \leq 10^9$.
• $0 \leq S_i < E_i \leq 10^9$ ($1 \leq i \leq N$).