#include <iostream>
#include <string>

using namespace std;

string IntToNum(int number, int base);
int StringToInt(string number, int base);
char DigitToChar(int digit);
int CharToDigit(char c);

int main() {
    int base,
        number;
    string otherRep;
    int convertBack;

    for (base = 2; base < 22; base += 3) {
        for(number = 2; number < 20; number ++) {
	     otherRep =   IntToNum(number, base);
	     convertBack = StringToInt(otherRep, base);

	     if (convertBack != number)  {
	         cout << "Error converting " << number 
		      << " to base " << base << " and back!" << endl;
	     }
	     cout << number << " in base " << base
	          << " is " << otherRep << endl;
	}
    }

    return 0;
}

char DigitToChar(int digit) {
    char returnValue;


    if (digit < 10) {
       returnValue = char('0' + digit);
    } else if (digit >= 10 and digit <= 36) {
       returnValue = char ('A' + digit-10);
    } else {
       cout << "Error converting " << digit << " to a char " << endl;
    }

    return returnValue;
}

int CharToDigit(char c) {
    int returnValue = 0;

    c = toupper(c);
    
    if ('0' <= c and c <= '9') {
        returnValue = c-'0';
    } else if ( 'A' <= c and c <= 'Z') {
        returnValue = 10+c-'A';
    } else {
        cout << "Error coverting '" << c << "' to a digit" << endl;
    }

    return returnValue ;
}

string IntToNum(int number, int base){
    string returnValue;
    int digit;
        

    while (number > 0) {
        digit = number % base;
	number = number / base;

	returnValue = DigitToChar(digit) + returnValue;
    }

    return returnValue;
}

int StringToInt(string number, int base){
    int returnValue=0;
    int i;

    for(i=0;i<number.size();i++) {
        returnValue  = returnValue * base + CharToDigit(number.at(i));
    }

    return returnValue;
}