URI 2158 - Helping Uncle Cláudio

The year is 1986 in a scientific publication was announced the discovery of a 3D carbon molecule, where the atoms occupy the vertices of a convex polyhedron with pentagonal and hexagonal faces, like a soccer ball.

In honor of Professor Claudio Carvalho, the molecule was named Claudeno. Claudio loves to check the amount of atoms and bonds in a given molecule. Today with the advanced age of the teacher he can not do the calculations "head" and asks you, the caregiver trainee elderly, create a program that can help.

Input

The entry consists of several test cases, each entry is composed of two integers, FP and FH (1 <FP, FH <10¹⁵), which represents the amount of pentagonais and hexagonal faces.

Output

Show to each molecule amount of atoms and their connections as shown in the sample output.

Input Sample	Output Sample
12 20 50 120 10025 548 468 17458	Molecula #1.:. Possui 60 atomos e 90 ligacoes Molecula #2.:. Possui 317 atomos e 485 ligacoes Molecula #3.:. Possui 16135 atomos e 26706 ligacoes Molecula #4.:. Possui 35620 atomos e 53544 ligacoes

Input Sample

Output Sample

12 20
50 120
10025 548
468 17458

Molecula #1.:.
Possui 60 atomos e 90 ligacoes

Molecula #2.:.
Possui 317 atomos e 485 ligacoes

Molecula #3.:.
Possui 16135 atomos e 26706 ligacoes

Molecula #4.:.
Possui 35620 atomos e 53544 ligacoes