Network

Time Limit: 2000 ms Memory Limit: 65536 KiB

Problem Description

 Andrew is working as system administrator and is planning to establish a new network in his
company. There will be N hubs in the company, they can be connected to each other using cables.
Since each worker of the company must have access to the whole network, each hub must be
accessible by cables from any other hub (with possibly some intermediate hubs).
Since cables of different types are available and shorter ones are cheaper, it is necessary to make
such a plan of hub connection, that the maximum length of a single cable is minimal. There is
another problem — not each hub can be connected to any other one because of compatibility
problems and building geometry limitations. Of course, Andrew will provide you all necessary
information about possible hub connections.
You are to help Andrew to find the way to connect hubs so that all above conditions are satisfied.
 

Input

 The first line of the input file contains two integer numbers: N — the number of hubs in the network
(2 ≤ N ≤ 1000) and M — the number of possible hub connections (1 ≤ M ≤ 15000). All hubs are
numbered from 1 to N. The following M lines contain information about possible connections —
the numbers of two hubs, which can be connected and the cable length required to connect them.
Length is a positive integer number that does not exceed 106. There will be no more than one way to
connect two hubs. A hub cannot be connected to itself. There will always be at least one way to
connect all hubs.
 

Output

 Output first the maximum length of a single cable in your hub connection plan (the value you
should minimize). Then output your plan: first output P — the number of cables used, then output P
pairs of integer numbers — numbers of hubs connected by the corresponding cable. Separate
numbers by spaces and/or line breaks.
 

Sample Input

4 6
1 2 1
1 3 1
1 4 2
2 3 1
3 4 1
2 4 1

Sample Output

1
4
1 2
1 3
2 3
3 4

Hint

 

Source

ACM ICPC 2001. Northeastern European Region, Northern Subregion