error: invalid user defined conversion from char to const key_type&

I am trying to assign int type value to each letter in latin alphabet using std::map. When I want to create new int and give it a value equal to int mapped to word, i get an error:

F:\Programming\korki\BRUDNOPIS\main.cpp|14|error: invalid user-defined conversion from 'char' to 'const key_type& {aka const std::basic_string&}' [-fpermissive]|

Example:

#include <iostream>
#include <string>
#include <cstdlib>
#include <map>

using namespace std;

int main()
{
    std::map <std::string,int> map;
    map["A"] = 1;
    int x;
    std:: string word = "AAAAAA";
    x = map[word[3]]

    cout << x;

    return 0;
}

What am I doing wrong?