The Settlers of Catan

Time Limit: 2 Seconds
Memory Limit: 65536 KB

Within Settlers of Catan, the 1995 German game of the year, players attempt to
dominate an island by building roads, settlements and cities across its uncharted
wilderness.

You are employed by a software company that just has decided to develop a computer
version of this game, and you are chosen to implement one of the game's special
rules:

When the game ends, the player who built the longest road gains two extra victory
points.

The problem here is that the players usually build complex road networks and
not just one linear path. Therefore, determining the longest road is not trivial
(although human players usually see it immediately).

Compared to the original game, we will solve a simplified problem here: You
are given a set of nodes (cities) and a set of edges (road segments) of length
1 connecting the nodes.

The longest road is defined as the longest path within the network that doesn't
use an edge twice. Nodes may be visited more than once, though.

Example: The following network contains a road of length 12.

o o--o o

\ / \ /

o--o o--o

/ \ / \

o o--o o--o

\ /

o--o

**Input**

The input will contain one or more test cases.

The first line of each test case contains two integers: the number of nodes
n (2 <= n <= 25) and the number of edges m (1 <= m <= 25). The next
m lines describe the m edges. Each edge is given by the numbers of the two nodes
connected by it. Nodes are numbered from 0 to n-1. Edges are undirected. Nodes
have degrees of three or less. The network is not neccessarily connected.

Input will be terminated by two values of 0 for n and m.

**Output**

For each test case, print the length of the longest road on a single line.

**Sample Input**

3 2

0 1

1 2

15 16

0 2

1 2

2 3

3 4

3 5

4 6

5 7

6 8

7 8

7 9

8 10

9 11

10 12

11 12

10 13

12 14

0 0

**Sample Output**

2

12

Source:

**University of Ulm Local Contest 1998**
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