Танцы синуса

#include <iostream>
#include <conio.h>
#include <string>
#include <math.h>
#include <algorithm>
#include <vector>
#include <set>
#include <sstream>

using namespace std;

string convertInt(int number)
{
    stringstream ss;
    ss << number;
    return ss.str();
}

string A(int n)
{
    string s="";
    for (int i = 1; i <= n; i++)
    {
        string prom = convertInt(i);
        if (i % 2 != 0)
        {
            s += "sin(";
            s += prom;
            if(i!=n)
            s += "-";
        }
        else
        {
            s += "sin(";
            s += prom;
            if (i != n)
            s += "+";
        }
    }
    for (int i = 1; i <= n; i++)
        s += ")";
    return s;
}


string S(int n)
{
    string res="";
    for (int i = 1; i <= n-1; i++)
        res += "(";
    for (int i = n; i >=2; i--)
    {
        string prom = convertInt(i);
        res += A(n - i + 1);
        res += "+";
        res += prom;
        res += ")";
    }
    res += A(n);
    res += "+1";
    return res;
}

int main()
{
    int n;

    cin >> n;

    cout << S(n);

    _getch();
    return 0;
}