Codeforces celebrates 10 years! We are pleased to announce the crowdfunding-campaign. Congratulate us by the link https://codeforces.com/10years.
×

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

D. BerDonalds

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBerDonalds, a well-known fast food restaurant, is going to open a cafe in Bertown. The important thing is to choose the new restaurant's location so that it would be easy to get there. The Bertown road system is represented by *n* junctions, connected by *m* bidirectional roads. For each road we know its length. We also know that we can get from any junction to any other one, moving along the roads.

Your task is to find such location of the restaurant, that the shortest distance along the roads from the cafe to the farthest junction would be minimum. Note that the restaurant can be located not only on the junction, but at any point of any road.

Input

The first line contains two integers *n* and *m* () — the number of junctions and the number of roads, correspondingly. Then *m* lines follow, describing all Bertown roads. Each road is described by three integers *a*_{i}, *b*_{i}, *w*_{i} (1 ≤ *a*_{i}, *b*_{i} ≤ *n*, *a*_{i} ≠ *b*_{i}; 1 ≤ *w*_{i} ≤ 10^{5}), where *a*_{i} and *b*_{i} are the numbers of the junctions, connected by the *i*-th road, and *w*_{i} is the length of the *i*-th road.

It is guaranteed that each road connects two distinct junctions, there is at most one road between any two junctions, and you can get from any junction to any other one.

Output

Print a single real number — the shortest distance from the optimal restaurant location to the farthest junction. The answer will be considered correct, if its absolute or relative error doesn't exceed 10^{ - 9}.

Examples

Input

2 1

1 2 1

Output

0.50

Input

3 3

1 2 1

2 3 1

1 3 1

Output

1.00

Input

3 2

1 2 100

2 3 1

Output

50.50

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/25/2020 22:58:57 (e2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|