There are n people numbered from $1$ to n in a town. There’s a rumor that one of these people is secretly the town judge. A town judge must meet the following conditions:

1. The judge doesn’t trust anyone.

2. Everyone else in the town (except the town judge) trusts the judge.

3. There is exactly one person who fulfills both the above conditions.

You are given an integer n and a two-dimensional array, trust, where each entry $trust[i] = [a_i, b_i]$ indicates that the person labeled $a_i$ trusts the person labeled $b_i$. If a trust relationship is not specified in the trust array, it does not exist. Your task is to determine the label of the town judge, if one can be identified. If no such person exists, return $-1$.

Constraints:

• $1 \leq$n $\leq 1000$

• $0 \leq$trust.length $\leq 10^{4}$

• trust[i].length $== 2$

• ai $\ne$ bi

• $1 \leq$ai , bi $\leq$n

• All the pairs in trust are unique.

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground: