The Town Judge Problem

In a town of n people labeled from 1 to n, there exists a rumor about a town judge. The town judge is defined by the following properties:

• The judge trusts no one.
• Every other person (except the judge) trusts the judge.

Formally, if the trust relationships are given as a list of ordered pairs \((a, b)\) (meaning person \(a\) trusts person \(b\)), then the town judge is the person \(j\) such that:

\[ \begin{cases} \text{trustCount}(j)=0\\ \text{trustedBy}(j)=n-1 \end{cases} \]

Note that if there is only one person in town and no trust relationships, then that person is the judge. If no such person exists, output \(-1\).

inputFormat

The input is given from stdin in the following format:

n
m
a1 b1
... 
am bm

Where:

• n is the number of people in the town.
• m is the number of trust relationships.
• Each of the next m lines contains two integers a and b (separated by space), indicating that person a trusts person b.

outputFormat

Output to stdout a single integer representing the label of the town judge if one exists, or \(-1\) if no judge exists.

## sample

1
0

1

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