Bee Garden

George's father Ben loves beekeeping. He keeps a bee garden near his country house and likes to walk around it gathering honey from the hives.

Ben has $n$ hives placed at various points of the garden. Some hives are connected to one another, or to Ben's house, by straight roads. Ben always walks along the roads and only ever switches from one road to another at a hive. Neither Ben's house nor any hive lies on a road.

The roads are arranged so that there is exactly one way to walk from the house to any given hive; that is, the house and the $n$ hives form a tree.

Every week Ben makes a round trip: he starts at his house, walks along the roads so that he visits every hive at least once, and returns home. He always takes the shortest such route.

To spare his aging father, George wants to build one extra straight road so that the round trip becomes as short as possible. The new road must connect two hives, or a hive and Ben's house. As with the existing roads, neither the house nor any hive may lie on the new road. Help George choose which road to build.

The first line contains $n$, the number of hives ($1 \le n \le 200$).

Place the garden on the Cartesian plane with Ben's house at the point $(0, 0)$. Each of the next $n$ lines contains two integers, the coordinates of one hive. Every coordinate is at most $10^4$ in absolute value, no two hives coincide, and no hive is at $(0, 0)$. The hives are numbered from $1$ to $n$.

Each of the following $n$ lines describes one existing road by the two nodes it connects, where $0$ denotes Ben's house and $1 \dots n$ denote the hives.

Print the two node numbers of the single new straight road that shortens the weekly round trip by the greatest amount, using $0$ for Ben's house and $1 \dots n$ for the hives. Print the smaller number first, separated by one space.

If several different roads shorten the round trip by the same maximum amount, print the lexicographically smallest such pair (compare the first number, then the second).

If no straight road can shorten the round trip, print -1.