The year is 2102 and today is the day of ZCO. This year there
are *N* contests and the starting and ending times of each
contest is known to you. You have to participate in exactly one
of these contests. Different contests may overlap. The duration
of different contests might be different.

There is only one examination centre. There is a wormhole
*V* that transports you from your house to the
examination centre and another wormhole *W* that
transports you from the examination centre back to your
house. Obviously, transportation through a wormhole does not take
any time; it is instantaneous. But the wormholes can be used at
only certain fixed times, and these are known to you.

So, you use a *V* wormhole to reach the exam centre,
possibly wait for some time before the next contest begins, take
part in the contest, possibly wait for some more time and then
use a *W* wormhole to return back home. If you leave
through a *V* wormhole at time *t*_{1} and
come back through a *W* wormhole at time
*t*_{2}, then the total time you have spent is
(*t*_{2} - *t*_{1} + 1). Your
aim is to spend as little time as possible overall while ensuring
that you take part in one of the contests.

You can reach the centre exactly at the starting time of the
contest, if possible. And you can leave the examination centre
the very second the contest ends, if possible. You can assume
that you will always be able to attend at least one
contest–that is, there will always be a contest
such that there is a *V* wormhole before it and a
*W* wormhole after it.

For instance, suppose there are 3 contests with (start,end)
times (15,21), (5,10), and (7,25), respectively. Suppose the
*V* wormhole is available at times 4, 14, 25, 2 and the
*W* wormhole is available at times 13 and 21. In this
case, you can leave by the *V* wormhole at time 14, take
part in the contest from time 15 to 21, and then use the
*W* wormhole at time 21 to get back home. Therefore the
time you have spent is (21 - 14 + 1) = 8. You
can check that you cannot do better than this.

The first line contains 3 space separated integers *N*,
*X*, and *Y*, where *N* is the number of
contests, *X* is the number of time instances when
wormhole *V* can be used and *Y* is the number of
time instances when wormhole *W* can be used. The next
*N* lines describe each contest. Each of these *N*
lines contains two space separated integers *S* and
*E*, where *S* is the starting time of the
particular contest and *E* is the ending time of that
contest, with *S* < *E*. The next line contains
*X* space separated integers which are the time instances
when the wormhole *V* can be used. The next line contains
*Y* space separated integers which are the time instances
when the wormhole *W* can be used.

Print a single line that contains a single integer, the minimum time needed to be spent to take part in a contest.

All the starting and ending times of contests are distinct and no contest starts at the same time as another contest ends. The time instances when wormholes are available are all distinct, but may coincide with starting and ending times of contests. All the time instances (the contest timings and the wormhole timings) will be integers between 1 and 1000000 (inclusive).

You may assume that
1 ≤ *N* ≤ 10^{5},
1 ≤ *X* ≤ 10^{5}, and
1 ≤ *Y* ≤ 10^{5}.

In 30% of the cases,
1 ≤ *N* ≤ 10^{3},
1 ≤ *X* ≤ 10^{3}, and
1 ≤ *Y* ≤ 10^{3}.

3 4 2 15 21 5 10 7 25 4 14 25 2 13 21

8

The time limit for this task is 1 second. The memory limit is 32MB.

Copyright (c) IARCS 2003-2018; Last Updated: 23 Sep 2012