Problem Statement

King Kazimierz is going to reorganize the road infrastructure in his kingdom. There are n towns in
the kingdom. The towns are labeled 0 through n-1. Some pairs of towns are connected by bidirectional
dirt roads. It is possible to travel between every pair of towns using the roads.

You are given a description of the roads in the int[]s e1 and e2. For each valid i, there is a road
between the towns e1[i] and e2[i].

The king wants to modernize all the roads. Unfortunately, after modernization the roads won't be
wide enough for two-way traffic, so each of the roads will have to become a one-way road. The king
now needs to choose the direction for each of the new one-way roads.

Kazimierz's adviser Zbyszek has prepared a list of strategic connections. You are given this list in
the int[]s s and t. For each valid i, being able to travel (either directly or indirectly) from the
town s[i] to the town t[i] is important for the country.

For any assignment of directions to the current roads we can compute its score: the number of
strategic connections that will be possible. Return the largest possible score.


Method signature: int getMax(int n, int[] e1, int[] e2, int[] s, int[] t)
Time limit (s): 2.000
Memory limit (MB): 256

Constraints

- n will be between 2 and 50, inclusive.
- e1 and e2 will have the same number of elements which will be between 1 and 500, inclusive.
- No road will appear twice. Pairs (u, v) and (v, u) describe the same road.
- There will be no loops i.e. for each pair (u, v) describing a road, u and v will be different.
- The graph represented by e1 and e2 will be connected.
- s and t will have the same number of elements which will be between 1 and 20, inclusive.
- No connection will appear twice. Pairs (u, v) and (v, u) describe different connections.
- For each i, t[i] and s[i] will be different.
- Each element of e1, e2, s and t will be between 0 and n - 1, inclusive.


Examples

0)

2
{0}
{1}
{0, 1}
{1, 0}
Returns: 1

We have two towns and a single road that connects them. We also have two strategic connections:
"getting from 0 to 1" and "getting from 1 to 0". Regardless of which direction we choose for the 0-1
road, we will only enable one of the two strategic connections.


1)

4
{0, 1, 2}
{2, 2, 3}
{0, 1, 3}
{3, 3, 2}
Returns: 2

An optimal solution here is to direct the roads as follows: from 0 to 2, from 1 to 2, and from 2 to
3. This will make two strategic connections possible: people will be able to travel from 0 to 3 (via
2), and they will be able to travel from 1 to 3 (also via 2).


2)

6
{0, 1, 1, 2, 3, 4}      
{1, 2, 3, 4, 4, 5}
{0, 5}
{4, 1}
Returns: 2

Here it is possible to have both strategic connections at the same time. One such solution is to
choose the directions 0->1, 1->2, 3->1, 2->4, 4->3, and 5->4. If the king chooses these directions
for the roads, people will be able to travel from 0 to 4 (via 1 and 2) and also from 5 to 1 (via 4
and 3).


3)

8
{0, 0, 1, 1, 3, 4, 4, 4}                
{1, 2, 2, 3, 4, 5, 6, 7}
{0, 1, 4, 5, 6}
{5, 7, 5, 0, 2}
Returns: 3


4)

20
{1, 2, 7, 9, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 19, 19}
{0, 1, 5, 8, 4, 3, 8, 9, 5, 7, 10, 4, 10, 0, 6, 14, 0, 15, 3, 9, 1, 1, 3, 11, 13}
{2, 6, 7, 9, 12, 13, 14, 16, 19, 19}
{7, 19, 12, 15, 16, 4, 7, 0, 13, 14}
Returns: 7


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