Input

There will be multiple test cases for this problem. Each test case will start with a pair of integers n (≤ 15) and m (≤ 20) on a line indicating the number of buildings (numbered 1 through n) and the number of potential inter-building connections, respectively. (Values of n = m = 0 indicate the end of the problem.) The following m lines are of the form b₁ b₂ c (all positive integers) indicating that it costs c to connect building b₁ and b₂. All connections are bidirectional.

Output

For each test case you should print one line giving the cost of a minimal reliable net. If there is a minimal reliable net, the output line should be of the form:

The minimal cost for test case p is c.

where p is the number of the test case (starting at 1) and c is the cost. If there is no reliable net possible, output a line of the form:

There is no reliable net possible for test case p.

Sample Input

4 5
1 2 1
1 3 2
2 4 2
3 4 1
2 3 1
2 1
1 2 5
0 0

Sample Output

The minimal cost for test case 1 is 6.
There is no reliable net possible for test case 2.