Counting the number of printable chars in a non-ascii string in C++

I want to check if a character is printable, but the input comes from the user so I cannot be sure it is ASCII. I tried to use the wide functions, but it does not work.

See this little program:

#include <iostream>
#include <clocale>
#include <string>

int main() {
    std::setlocale(LC_ALL, "");

    std::wstring str{};
    std::wcin >> str;
    std::wcout << "\n";

    for (auto& c : str) {
        if (std::isprint(c))
            std::wcout << c << "  is printable\n";
        else
            std::wcout << c << "  is NOT printable\n";
    }

    std::wcout "\n" << str << std::endl;

}

It compiles fine, but the result works only for the second and third character!

% ./test
かたな

か  is NOT printable
た  is printable
な  is printable

かたな

What am I missing? Is there a way to check if a character is printable that works from standard input whatever locale is there? Or something more generic depending on the encoding?