Problem E: Flea circus

Sometimes, if you are searching for ladybugs, all you find are tree fleas. An old tree near the anthill serves as a home of two fleas who sometimes steal honeydew from aphids living on the tree. On the old tree, branches connect the forks (spaces where two or more branches meet) and leaves where the fleas can rest. Fleas are so small that the ants cannot see them and thus fleas are safe. Because of their size, the fleas satiate their appetite pretty quickly and then have a lot of energy to jump. They decide to jump toward each other complying with the following rules:

The input file contains multiple test cases. Each test case starts with an integer n, the number of leaves and forks in the tree, 1≤n≤5000. We assume that leaves and forks are numbered from 1 to n. Each of the following n-1 lines describe tree branches; each branch is described by two integers a and b, meaning that the branch connects the fork or leaf labeled a and the fork or leaf labeled b. In the (n+1)-st line there is one integer l, 1≤l≤500, saying how many starting positions of the fleas you are to consider for the tree. Each of the following l lines contains two positive integers (not greater than n). These numbers define the tree places in which the fleas start their jumping. Input is terminated by the case with n equal to 0.

Your program should output l lines for each test case. The i-th line for a case should look like

The fleas meet at p.

where p identifies the place where the fleas meet, or

The fleas jump forever between p and r.

where p and r are two neighboring places on the tree with p ≤ r

Sample input

1 2
1 3
2 4
2 5
3 6 
3 7
5 8
5 1 
7 4
1 8
4 7
7 8

Output for sample input

The fleas meet at 2.
The fleas meet at 1.
The fleas jump forever between 2 and 5.
The fleas meet at 1.
The fleas jump forever between 1 and 2.

Piotr Rudnicki
ACPC 2005