Problem BK
All Pairs Shortest Path

Input

The input consists of several test cases. Each test case starts with a line with three non-negative integers, $1 \le n \le 150$, $0 \le m \le 5000$ and $1 \le q \le 1000$, separated by single single spaces, where $n$ is the numbers of nodes in the graph, $m$ the number of edges and $q$ the number of queries. Nodes are numbered from $0$ to $n-1$. Then follow $m$ lines, each line consisting of three (space-separated) integers $u$, $v$ and $w$ indicating that there is an edge from $u$ to $v$ in the graph with weight $-1000 \le w \le 1000$. Then follow $q$ lines of queries, each consisting of two node numbers $u$ and $v$ (separated by a space), asking for the minimum distance from node $u$ to node $v$.

Input will be terminated by a line containing 0 0 0, this line should not be processed.

Output

For each query, output a single line containing the minimum distance from node $u$ to $v$, or the word Impossible if there is no path from $u$ to $v$, or -Infinity if there are arbitrarily short paths from $u$ to $v$. Print a blank line after each test case.

4 3 4
0 1 2
1 2 2
3 3 1
0 2
1 2
3 0
3 3
2 1 2
0 1 100
0 1
1 0
0 0 0

4
2
Impossible
0

100
Impossible