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.

×
E. Pumping Stations

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMad scientist Mike has applied for a job. His task is to manage a system of water pumping stations.

The system consists of *n* pumping stations, which are numbered by integers from 1 to *n*. Some pairs of stations are connected by bidirectional pipes through which water can flow in either direction (but only in one at a time). For each pipe you know its bandwidth — the maximum number of liters of water that can flow through it in one hour. Each pumping station can pump incoming water from some stations to other stations through the pipes, provided that in one hour the total influx of water to the station is equal to the total outflux of water from the station.

It is Mike's responsibility to pump water between stations. From station *a* to station *b* through the pipes (possibly through other stations) within one hour one can transmit a certain number of liters of water according to the rules described above. During this time, water from other stations can not flow into station *a*, and can not flow out of the station *b*. However, any amount of water can flow out of station *a* or in station *b*. If a total of *x* litres of water flows out of the station *a* in an hour, then Mike gets *x* bollars more to his salary.

To get paid, Mike needs to work for *n* - 1 days, according to the contract. On the first day he selects two stations *v*_{1} and *v*_{2}, and within one hour he pumps a certain amount of water from *v*_{1} to *v*_{2}. Next, on the *i*-th day Mike chooses a station *v*_{i + 1} that has been never selected before, and pumps a certain amount of water out of the station *v*_{i} to station *v*_{i + 1} for one hour. The quantity of water he pumps on the *i*-th day does not depend on the amount of water pumped on the (*i* - 1)-th day.

Mike needs to earn as much bollars as he can for his projects. Help Mike find such a permutation of station numbers *v*_{1}, *v*_{2}, ..., *v*_{n} so Mike will be able to earn the highest possible salary.

Input

The first line of the input contains two space-separated integers *n* and *m* (2 ≤ *n* ≤ 200, 1 ≤ *m* ≤ 1000) — the number of stations and pipes in the system, accordingly. The *i*-th of the next *m* lines contains three space-separated integers *a*_{i}, *b*_{i} and *c*_{i} (1 ≤ *a*_{i}, *b*_{i} ≤ *n*, *a*_{i} ≠ *b*_{i}, 1 ≤ *c*_{i} ≤ 100) — the numbers of stations connected by the *i*-th pipe and the pipe's bandwidth, accordingly. It is guaranteed that any two stations are connected by at most one pipe and that there is a pipe path between any two stations.

Output

On the first line print a single integer — the maximum salary Mike can earn.

On the second line print a space-separated permutation of *n* numbers from 1 to *n* — the numbers of stations in the sequence *v*_{1}, *v*_{2}, ..., *v*_{n}. If there are multiple answers, print any of them.

Examples

Input

6 11

1 2 10

1 6 8

2 3 4

2 5 2

2 6 3

3 4 5

3 5 4

3 6 2

4 5 7

4 6 2

5 6 3

Output

77

6 2 1 5 3 4

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/11/2021 14:01:19 (i1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|