我重载了operator<<以打印向量中的所有元素，但它不工作吗？

#include <iostream>
#include <vector>

template <typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& vec) {
    os << "[";
    for (size_t i = 0; i < vec.size(); ++i) {
        os << vec[i];
        if (i != vec.size() - 1) {
            os << ", ";
        }
    }
    os << "]";
    return os;
}

int main() {
    std::vector<int> vec = {1, 2, 3, 4, 5};
    std::cout << vec << std::endl;  // 输出: [1, 2, 3, 4, 5]
    return 0;
}

class MyClass {
private:
    std::vector<int> data;

public:
    friend std::ostream& operator<<(std::ostream& os, const MyClass& obj);
};

std::ostream& operator<<(std::ostream& os, const MyClass& obj) {
    os << "[";
    for (size_t i = 0; i < obj.data.size(); ++i) {
        os << obj.data[i];
        if (i != obj.data.size() - 1) {
            os << ", ";
        }
    }
    os << "]";
    return os;
}