Loud and Rich

There is a group of n people labeled from 0 to n - 1 where each person has a different amount of money and a different level of quietness.

You are given an array richer where richer[i] = [ai, bi] indicates that ai has more money than bi, and an integer array quiet where quiet[i] is the quietness of the i^th person. All the given data in richer are logically correct; that is, the data will not lead to a situation where x is richer than y and y is richer than x at the same time.

Return an integer array answer where answer[x] = y if y is the least quiet person, meaning the person y with the smallest value of quiet[y], among all people who definitely have equal to or more money than person x.

Example 1
Inputricher = [[1,0],[2,1],[3,1],[3,7],[4,3],[5,3],[6,3]], quiet = [3,2,5,4,6,1,7,0]
Output[5,5,2,5,4,5,6,7]
Person 5 is the quietest among all people definitely as rich as person 0, person 7 is quietest among all people definitely as rich as person 7, and the other entries follow similarly.
Example 2
Inputricher = [], quiet = [0]
Output[0]
With only one person and no richer relationships, person 0 is the quietest person with at least as much money as themself.

Constraints

  • n == quiet.length
  • 1 <= n <= 500
  • 0 <= quiet[i] < n
  • All the values of quiet are unique.
  • 0 <= richer.length <= n * (n - 1) / 2
  • 0 <= ai, bi < n
  • ai != bi
  • All the pairs of richer are unique.
  • The observations in richer are all logically consistent.

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