#P993B. Open Communication
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ID: 4300
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Open Communication
No submission language available for this problem.
Description
Two participants are each given a pair of distinct numbers from 1 to 9 such that there's exactly one number that is present in both pairs. They want to figure out the number that matches by using a communication channel you have access to without revealing it to you.
Both participants communicated to each other a set of pairs of numbers, that includes the pair given to them. Each pair in the communicated sets comprises two different numbers.
Determine if you can with certainty deduce the common number, or if you can determine with certainty that both participants know the number but you do not.
The first line contains two integers $n$ and $m$ ($1 \le n, m \le 12$) — the number of pairs the first participant communicated to the second and vice versa.
The second line contains $n$ pairs of integers, each between $1$ and $9$, — pairs of numbers communicated from first participant to the second.
The third line contains $m$ pairs of integers, each between $1$ and $9$, — pairs of numbers communicated from the second participant to the first.
All pairs within each set are distinct (in particular, if there is a pair $(1,2)$, there will be no pair $(2,1)$ within the same set), and no pair contains the same number twice.
It is guaranteed that the two sets do not contradict the statements, in other words, there is pair from the first set and a pair from the second set that share exactly one number.
If you can deduce the shared number with certainty, print that number.
If you can with certainty deduce that both participants know the shared number, but you do not know it, print $0$.
Otherwise print $-1$.
Input
The first line contains two integers $n$ and $m$ ($1 \le n, m \le 12$) — the number of pairs the first participant communicated to the second and vice versa.
The second line contains $n$ pairs of integers, each between $1$ and $9$, — pairs of numbers communicated from first participant to the second.
The third line contains $m$ pairs of integers, each between $1$ and $9$, — pairs of numbers communicated from the second participant to the first.
All pairs within each set are distinct (in particular, if there is a pair $(1,2)$, there will be no pair $(2,1)$ within the same set), and no pair contains the same number twice.
It is guaranteed that the two sets do not contradict the statements, in other words, there is pair from the first set and a pair from the second set that share exactly one number.
Output
If you can deduce the shared number with certainty, print that number.
If you can with certainty deduce that both participants know the shared number, but you do not know it, print $0$.
Otherwise print $-1$.
Samples
2 2
1 2 3 4
1 5 3 4
1
2 2
1 2 3 4
1 5 6 4
0
2 3
1 2 4 5
1 2 1 3 2 3
-1
Note
In the first example the first participant communicated pairs $(1,2)$ and $(3,4)$, and the second communicated $(1,5)$, $(3,4)$. Since we know that the actual pairs they received share exactly one number, it can't be that they both have $(3,4)$. Thus, the first participant has $(1,2)$ and the second has $(1,5)$, and at this point you already know the shared number is $1$.
In the second example either the first participant has $(1,2)$ and the second has $(1,5)$, or the first has $(3,4)$ and the second has $(6,4)$. In the first case both of them know the shared number is $1$, in the second case both of them know the shared number is $4$. You don't have enough information to tell $1$ and $4$ apart.
In the third case if the first participant was given $(1,2)$, they don't know what the shared number is, since from their perspective the second participant might have been given either $(1,3)$, in which case the shared number is $1$, or $(2,3)$, in which case the shared number is $2$. While the second participant does know the number with certainty, neither you nor the first participant do, so the output is $-1$.