A celebrity in a social network is somebody with many followers, but who doesn't follow them back. More precisely, a person is a for a group of people, if
every member of the group follows the person,
the person follows nobody in the group.
The of person , written , is the maximum size of such a group.
We model the social network as a directed graph with vertices , , . A directed edge from to means that person follows person . For example, in
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we have , , and .
Your task is to find a vertex with the maximum celebrity centrality . In case of a tie, choose the smallest .
输入格式
The input consists of
One line with two integers and (, ), the number of vertices and the number of directed edges.
lines with two distinct integers and (), indicating a directed edge from to . There are no duplicate edges.
输出格式
Output two integers: the smallest with the maximum celebrity centrality and the value .
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