Find the Town Judge

The key idea

The judge is trusted by everyone else and trusts nobody. Give each person +1 when someone trusts them and -1 when they trust someone. The judge is the one and only person whose net score equals n - 1.

Problem

In a town of n people labeled from 1 to n, there is a rumor that one of these people is secretly the town judge.

If the town judge exists, then:

1. The town judge trusts nobody.
2. Everybody (except the town judge) trusts the town judge.
3. There is exactly one person that satisfies properties 1 and 2.

You are given an array trust where trust[i] = [a, b] means that the person labeled a trusts the person labeled b. If a trust relationship does not exist in trust array, then such a trust relationship does not exist.

Return the label of the town judge if the town judge exists and can be identified, or return -1 otherwise.

Constraints

1 <= n <= 1000
0 <= trust.length <= 10^4
trust[i].length == 2
All the pairs of trust are unique.
trust[i][0] != trust[i][1]
1 <= trust[i][0], trust[i][1] <= n

Examples

Input: n = 2, trust = [[1,2]] Output: 2

Input: n = 3, trust = [[1,3],[2,3]] Output: 3

Input: n = 3, trust = [[1,3],[2,3],[3,1]] Output: -1

Complexity

Time: O(n + e) Space: O(n)

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