Merge Sort - C++ (Rough)

#include <iostream>
#include <string>
#include <vector>
#include <cstdlib>

using namespace std;

void mergesort(vector<char>& vec) {
    int n = vec.size();

    // recursion terminator
    if (n <= 1) return;
    else if (n == 2) {
        if (vec[0] > vec[1]) {

            char tmp = vec[0];
            vec[0] = vec[1];
            vec[1] = tmp;

        }

        return;
    }

    vector<char> left(vec.begin(), vec.begin() + n / 2);
    vector<char> right(vec.begin() + n / 2, vec.end());
    vec.erase(vec.begin(), vec.end()); // because we have copied the values to the partitions (left and right)

    mergesort(left); mergesort(right);

    int itr = 0;

    while(!left.empty() && !right.empty() && itr < n) {
        if (left[0] < right[0]) {

            vec.push_back(left.front());

            left.erase(left.begin());
        } else {

            vec.push_back(right.front());

            right.erase(right.begin());
        }

        itr++;
    }

    if (!left.empty()) {
        vec.insert(vec.end(), left.begin(), left.end());
    } else if (!right.empty()) {
        vec.insert(vec.end(), right.begin(), right.end());
    }

}

int main() {
    cout << "give me a string" << endl;
    string s; getline(cin, s);

    vector<char> vec(s.begin(), s.end());

    if (!vec.empty()) mergesort(vec);

    string str(vec.begin(), vec.end());

    cout << str << endl;
    return 0;
}