Use std::type_index as value in a map

I am trying to create a std::unordered_map where the value is a std::type_index. The following snippet works:

std::unordered_map<std::type_index, int> workingMap;
workingMap[typeid(int)] = 1;
workingMap[typeid(char)] = 2;

But this one doesn't run and throws an error:

std::unordered_map<int, std::type_index> failingMap;
failingMap[1] = typeid(int);
failingMap[2] = typeid(char);

CS2512: 'std::type_index::type_index': no appropriate default constructor available.

I don't fully understand this error, what is the difference between the constructors in these examples? Is it possible to make a map where typeid(..) is the value instead of the key?