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

E. Dead Ends

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLife in Bertown has become hard. The city has too many roads and the government spends too much to maintain them. There are *n* junctions and *m* two way roads, at which one can get from each junction to any other one. The mayor wants to close some roads so that the number of roads left totaled to *n* - 1 roads and it were still possible to get from each junction to any other one. Besides, the mayor is concerned with the number of dead ends which are the junctions from which only one road goes. There shouldn't be too many or too few junctions. Having discussed the problem, the mayor and his assistants decided that after the roads are closed, the road map should contain exactly *k* dead ends. Your task is to count the number of different ways of closing the roads at which the following conditions are met:

- There are exactly
*n*- 1 roads left. - It is possible to get from each junction to any other one.
- There are exactly
*k*dead ends on the resulting map.

Two ways are considered different if there is a road that is closed in the first way, and is open in the second one.

Input

The first line contains three integers *n*, *m* and *k* (3 ≤ *n* ≤ 10, *n* - 1 ≤ *m* ≤ *n*·(*n* - 1) / 2, 2 ≤ *k* ≤ *n* - 1) which represent the number of junctions, roads and dead ends correspondingly. Then follow *m* lines each containing two different integers *v*_{1} and *v*_{2} (1 ≤ *v*_{1}, *v*_{2} ≤ *n*, *v*_{1} ≠ *v*_{2}) which represent the number of junctions connected by another road. There can be no more than one road between every pair of junctions. The junctions are numbered with integers from 1 to *n*. It is guaranteed that it is possible to get from each junction to any other one along the original roads.

Output

Print a single number — the required number of ways.

Examples

Input

3 3 2

1 2

2 3

1 3

Output

3

Input

4 6 2

1 2

2 3

3 4

4 1

1 3

2 4

Output

12

Input

4 6 3

1 2

2 3

3 4

4 1

1 3

2 4

Output

4

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Nov/12/2019 12:37:47 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|