Long arithmetic

#include "stdafx.h"
#include "iostream"
#include "fstream"
#include "string"
using namespace std;

bool compareTwoLongNumbers(string first, char sign, string second);
void input(string &first_number, char &sign, string &second_number);
void output(bool result);


int _tmain(int argc, _TCHAR* argv[])
{
    string first_number, second_number;
    char sign;
    input(first_number, sign, second_number);

    output(compareTwoLongNumbers(first_number, sign, second_number));
    system("pause");
}

bool compareTwoLongNumbers(string first_number, char sign, string second_number){
    if (first_number == second_number){
        if (sign == '=') { return true; }
        return false;
    }
    else {
        int flag;
        if (first_number.length() > second_number.length()){ flag = true; }
        else if (first_number.length() < second_number.length()) { flag = false; }
        else {
            for (int i = 0; i < (int)first_number.length(); i++){
                if (first_number[i] > second_number[i]){
                    flag = true;
                    break;
                }
                else if (first_number[i] < second_number[i]){
                    flag = false;
                    break;
                }
            }
        }
        if ((flag && sign == '>') || (!flag && sign == '<')){ return true; }
        return false;
    }
};

void input(string &first_number, char &sign, string &second_number){
    string filename;
    cin >> filename;

    ifstream input(filename);
    ofstream errors("errors.txt");

    if (!input){
        errors << "Can't open the file" << endl;
        cout << "Can't open the file" << endl;
        exit(0);
    }

    input >> first_number >> sign >> second_number;
    input.close();
}
void output(bool result){
    ofstream output("output.txt");
    if (result) {
        output << "The expression is true." << endl;
    }
    else {
        output << "The expression is false." << endl;
    }
    output.close();
}