// Program to calculate integer results without using int types.
 
// Define the digits. //
using namespace std;
char digits[]=  {'0','1','2','3','4','5','6','7','8','9','\0'};
char one[]=  {'1', '\0'};
char zero[]=  {'0', '\0'};

// Prototypes for functions that perform integer calculations. // 
char* sum( char a[], char b[] );		// Returns a + b
char* diff( char a[], char b[] );		// Returns a - b
char* product( char a[], char b[] );	// Returns a * b
bool equal( char a[], char b[] );		// True iff a == b

// Now, code the functions to perform arithmetic. //
int length( char a[]) {
	int j=0;
	while ( a[j] !='\0') ++j;	// Find null terminator.
	return j;
}
char* sum( char a[], char b[] )		// Returns a + b
{
	int lsum=  length(1) + length(b) ;
	char result[  lsum ];
       	result[0]= '\0';
	for (int j=0; j<length(a); ++j )
	{
		// ++++ WRITE YOUR OWN CODE HERE +++
	}
	return result;
}

// Function to calculate factorial (recursively). //
char* factorial( char n[] ) {
	if (equal( n, zero )) return one;			// 0! is 1
	if (equal( n, zero )) return one;			// 1! is 1
	return product( n, factorial( diff(n,one) ) );	// n! = n*(n-1)!
}

// . . .
// ++++ ADD YOUR OWN CODE BELOW +++

int main()
{
		// ++++ WRITE YOUR OWN CODE HERE +++	
}