Colored Paper

There are six kinds of square colored paper whose side lengths are 1cm, 2cm, 3cm, 4cm, 5cm, and 6cm. A sheet of type k has side length kcm.

Figure 1

All sheets must be attached to boards that are 6cm wide and 6cm tall. A sheet must not cross the boundary of a board, and two sheets must not overlap. Each sheet must fit completely inside a single board.

Figure 2

Given the number of sheets of each size, find the minimum number of 6cm × 6cm boards needed to attach all of them.

Six lines are given. From the first line to the sixth line, they contain the numbers of type 1 through type 6 colored papers in order. Each count is at most 100.

Print the minimum number of boards needed to attach all the colored papers.