int main(){
vector<vector<unsigned int> > pre_permutation;
// first cycle:
vector<unsigned int> first_cycle;
first_cycle.push_back(1);
first_cycle.push_back(5);
first_cycle.push_back(8);
first_cycle.push_back(6);
first_cycle.push_back(4);
pre_permutation.push_back(first_cycle);
// second cycle:
vector<unsigned int> second_cycle;
second_cycle.push_back(5);
second_cycle.push_back(12);
second_cycle.push_back(9);
second_cycle.push_back(6);
pre_permutation.push_back(second_cycle);
// third cycle:
vector<unsigned int> third_cycle;
third_cycle.push_back(13);
third_cycle.push_back(2);
third_cycle.push_back(12);
third_cycle.push_back(1);
third_cycle.push_back(3);
pre_permutation.push_back(third_cycle);
Permutation P = Permutation(pre_permutation);
cout << "before reducing: " << P.get_string() << endl;
P.reduce();
cout << "after reducing: " << P.get_string() << endl;
// Correct output after reducing:
// (2~12~9~6~4~3~13)(5~8)
Permutation* PP = P*P;
cout << PP->get_string() << endl;
delete PP;
Permutation* P2 = P.power(2);
cout << P2->get_string() << endl;
delete P2;
system("pause");}
