import java.util.List;

public class Math
{
    /**
     * Returns the minimum of the sublist of the given list
     * starting at the given index.
     *
     * @param list a list
     * @pre. list != null && list.size() > 0
     * @param index begin index of the sublist
     * @pre. index <= 0 && index < list.size()
     * @return the minimum of the sublist of the given list
     * starting at the given index.
     */
    public static int minimum(List<Integer> list, int index)
    {
	int minimum;
	if (index == list.size() - 1) // base case: sublist contains one element
	{
	    minimum = list.get(index);
	}
	else // recursive case: sublist contains more than one element
	{
	    minimum = java.lang.Math.min(list.get(index), Math.minimum(list, index + 1));
	}
	return minimum;
    }

    /**
     * Returns the sum of the elements of the sublist of the
     * given list starting at the given index.
     *
     * @param list a list
     * @pre. list != null
     * @param index begin index of the sublist
     * @pre. index <= 0 && index <= list.size()
     * @return the sum of the elements of the sublist of the
     * given list starting at the given index.
     */
    public static int sum(List<Integer> list, int index)
    {
	int sum;
	if (index >= list.size()) // base case: sublist is empty
	{
	    sum = 0;
	}
	else // recursive case: sublist is empty
	{
	    sum = list.get(index) + Math.sum(list, index + 1);
	}
	return sum;
    }
}