range-based access of modified elements

This is a simplified instance of actual code. The goal was to provide access to container elements via range-based loops BUT have the elements changed on-the-fly (here ints are squared) without exposing the change.

The code works but seems overly complicated and unreadable. What simplification did I miss?

#include <vector>
#include <iostream>

using ivec_t = std::vector<int>;
class A {
    ivec_t vec;
public:
    A(const ivec_t& v) : vec(v) {}
    class sq_class {
        class iter {
            ivec_t::iterator ivit;
        public:
            iter(ivec_t::iterator the_ivit) : ivit(the_ivit) {}
            bool operator!=(const iter& other) { return ivit != other.ivit; }
            iter& operator++()                 { ++ivit; return *this; }
            int operator*()                    { return (*ivit)*(*ivit); } // <-------------------
        };
        ivec_t ivec;
    public:
        sq_class(ivec_t& the_ivec) : ivec(the_ivec) {}
        iter begin()   { return iter(ivec.begin()); }
        iter end()     { return iter(ivec.end()); }
    };
    sq_class squares() { return sq_class(vec); }
};

main()
{
    A a({1,2,4});

    // expected output: 1, 4, 16,
    for (auto item : a.squares())
        std::cerr << item << ", ";

    std::cerr << "\n";
}