Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Police Station

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe Berland road network consists of *n* cities and of *m* bidirectional roads. The cities are numbered from 1 to *n*, where the main capital city has number *n*, and the culture capital — number 1. The road network is set up so that it is possible to reach any city from any other one by the roads. Moving on each road in any direction takes the same time.

All residents of Berland are very lazy people, and so when they want to get from city *v* to city *u*, they always choose one of the shortest paths (no matter which one).

The Berland government wants to make this country's road network safer. For that, it is going to put a police station in one city. The police station has a rather strange property: when a citizen of Berland is driving along the road with a police station at one end of it, the citizen drives more carefully, so all such roads are considered safe. The roads, both ends of which differ from the city with the police station, are dangerous.

Now the government wonders where to put the police station so that the average number of safe roads for all the shortest paths from the cultural capital to the main capital would take the maximum value.

Input

The first input line contains two integers *n* and *m* (2 ≤ *n* ≤ 100, ) — the number of cities and the number of roads in Berland, correspondingly. Next *m* lines contain pairs of integers *v*_{i}, *u*_{i} (1 ≤ *v*_{i}, *u*_{i} ≤ *n*, *v*_{i} ≠ *u*_{i}) — the numbers of cities that are connected by the *i*-th road. The numbers on a line are separated by a space.

It is guaranteed that each pair of cities is connected with no more than one road and that it is possible to get from any city to any other one along Berland roads.

Output

Print the maximum possible value of the average number of safe roads among all shortest paths from the culture capital to the main one. The answer will be considered valid if its absolute or relative inaccuracy does not exceed 10^{ - 6}.

Examples

Input

4 4

1 2

2 4

1 3

3 4

Output

1.000000000000

Input

11 14

1 2

1 3

2 4

3 4

4 5

4 6

5 11

6 11

1 8

8 9

9 7

11 7

1 10

10 4

Output

1.714285714286

Note

In the first sample you can put a police station in one of the capitals, then each path will have exactly one safe road. If we place the station not in the capital, then the average number of safe roads will also make .

In the second sample we can obtain the maximum sought value if we put the station in city 4, then 6 paths will have 2 safe roads each, and one path will have 0 safe roads, so the answer will equal .

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/25/2021 10:26:01 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|