Each representation of a BAGG consists of the following sections,
separated by whitespaces.
1. The number of Players, n.
2. The number of action nodes, |S|.
3. The number of function nodes, |P|.
4. The number of types for each player, as a row of n integers.
5. Type distribution for each player. The distributions are assumed to be independent.
Each distribution is represented as a row of real numbers.
6. Size of type-action set for each player's each type.
7. Type-action set for each player's each type.
Each type-action set is represented as a row of integers in ascending order,
which are indices of action nodes. Action nodes are indexed from 0 to S-1.
8. The action graph: same as in the AGG format. See the AGGFORMAT file for details.
9. types of functions: same as in the AGG format.
10. utility function for each action node: same as in the AGG format.