Colored Paper

Time limit1sMemory limit128 MB

Summary

Given counts of six square sizes (1-6 cm), determine the minimum number of 6x6 boards needed to place all squares without overlap or crossing edges.

Level: Medium6 of 10
Topics: Greedy, Math, Simulation
Solved: No attempts yet

Problem

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.

Input

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.

Output

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

Examples1

Example 1
Input
```
5
3
0
1
1
0
```
Expected output
```
2
```