## ACPC10D - Tri graphs

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Here’s a simple graph problem: Find the shortest path from the top-middle vertex to the bottom-middle vertex in a given tri-graph. A tri-graph is an acyclic graph of (N ≥ 2) rows and exactly 3 columns. Unlike regular graphs, the costs in a tri-graph are associated with the vertices rather than the edges.

So, considering the example with N = 4, the cost of going straight down from the top to bottom along the middle vertices is 7 + 13 + 3 + 6 = 29. The layout of the directional edges in the graph are always the same as illustrated in the figure.

### Input

Your program will be tested on one or more test cases.
Each test case is specified using N + 1 lines where the first line specifies a single integer (2 ≤ N ≤ 100, 000) denoting the number of rows in the graph. N lines follow, each specifying three integers representing the cost of the vertices on the ith row from left to right. The square of each cost value is less than 1,000,000.
The last case is followed by a line with a single zero.

### Output

For each test case, print the following line:
k. n
Where k is the test case number (starting at one,) and n is the least cost to go from the top-middle vertex to the bottom-middle vertex.

### Example

`Input:413 7 57 13 614 3 1215 6 160Output:1. 22`

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 Rajat (1307086): 2015-01-29 21:39:49 DP :) a classical one...... V Y: 2015-01-16 09:20:59 Check out that output format. Fabian Conejo: 2015-01-08 01:27:08 In: 1 2 -2 1 1 1 Out: 1 ankit bisla: 2014-12-20 20:17:43 Last edit: 2014-12-20 20:20:00 swordfish12: 2014-12-17 16:57:34 good dp for beginners ANSHUL ARZARE: 2014-12-13 12:01:55 Easy but Nice problem :) « sudipto »: 2014-11-11 19:31:12 AC after lots and lots of WA.... negative numbers should have been mentioned..... :/ .... still a lovely problem.... :) Manoj Kumar Regar: 2014-10-24 12:53:37 Getting Wrong ans!..... so sad! consider these.... 1. negative nos. may be there 2. never consider top-left square in your dp or sol. check this .. 2 4 5 6 4 4 4 2 -1 -1 -1 -1 -1 -1 op 1. 9 2. -3 Last edit: 2014-10-24 12:54:12 Arun Karthikeyan: 2014-10-10 21:56:03 Simple DP codedog: 2014-08-24 00:33:50 someone please help me,my program runs fine on my ide and passes all test cases.

 Added by: Omar ElAzazy Date: 2010-11-30 Time limit: 1s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM64 Resource: ACPC 2010