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

F2. Script Generation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe Smart Beaver from ABBYY was offered a job of a screenwriter for the ongoing TV series. In particular, he needs to automate the hard decision: which main characters will get married by the end of the series.

There are *n* single men and *n* single women among the main characters. An opinion poll showed that viewers like several couples, and a marriage of any of them will make the audience happy. The Smart Beaver formalized this fact as *k* triples of numbers (*h*, *w*, *r*), where *h* is the index of the man, *w* is the index of the woman, and *r* is the measure of the audience's delight in case of the marriage of this couple. The same poll showed that the marriage of any other couple will leave the audience indifferent, so the screenwriters decided not to include any such marriages in the plot.

The script allows you to arrange several marriages between the heroes or not to arrange marriages at all. A subset of some of the *k* marriages is considered acceptable if each man and each woman is involved in at most one marriage of the subset (the series won't allow any divorces). The value of the acceptable set of marriages is the total delight the spectators will get from the marriages included in this set.

Obviously, there is a finite number of acceptable sets, and they all describe some variants of the script. The screenwriters do not want to choose a set with maximum value — it would make the plot too predictable. So the Smart Beaver offers the following option: sort all the acceptable sets in increasing order of value and choose the *t*-th set from the sorted list. Thus, *t* = 1 corresponds to a plot without marriages, *t* = 2 — to a single marriage resulting in minimal delight for the audience, and so on.

Help the Beaver to implement the algorithm for selecting the desired set.

Input

The first input line contains integers *n*, *k* and *t* (1 ≤ *k* ≤ *min*(100, *n*^{2}), 1 ≤ *t* ≤ 2·10^{5}), separated by single spaces. Next *k* lines contain triples of integers (*h*, *w*, *r*) (1 ≤ *h*, *w* ≤ *n*; 1 ≤ *r* ≤ 1000), separated by single spaces, which describe the possible marriages. It is guaranteed that the input data is correct: *t* doesn't exceed the total number of acceptable sets, and each pair (*h*, *w*) is present in at most one triple.

The input limitations for getting 30 points are:

- 1 ≤
*n*≤ 5

The input limitations for getting 100 points are:

- 1 ≤
*n*≤ 20

Output

Print a single number — the value of the *t*-th acceptable variant.

Examples

Input

2 4 3

1 1 1

1 2 2

2 1 3

2 2 7

Output

2

Input

2 4 7

1 1 1

1 2 2

2 1 3

2 2 7

Output

8

Note

The figure shows 7 acceptable sets of marriages that exist in the first sample.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/22/2020 10:14:15 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|