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ZOJ Problem Set - 1173
Water Glass

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Steve is a glass blower. He has an order to make water glass (clocks) from one very eccentric lady. Because that person is eccentric she does not want her water glass have usual form. Instead she would like one made of two symmetric prisms based on some polygon. Of course that polygon has a base side the glass should stand on and single vertex the water should flow through. As a good professional Steve has made what he has been asked for but he has difficulties to calculate where the time measures should be marked. Assume the water is flowing evenly through the hole, the upper prism is full with the water in the initial time, all the water completely flows into the lower prism in exactly 24 hours. You are to write program that being given the form of the polygon calculates the water level in the lower prism each half-hour period starting from initial time.

This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between output blocks.

Input

Input starts with a single line containing 3 <= N <= 20 - number of vertices in the polygon. Next N lines each contain 2 integers -50 <= xi <= 50 and 0 <= yi <= 50 - coordinates of ith vertex. Note that x1, y1 are coordinates of the vertex the water would flow through. You can assume the following conditions are true: if (xk, yk), (xk+1, yk+1) - coordinates of the vertices that form the glass base then

1. yk = yk+1 = 0
2. For all 1 < i < k, yi < yi-1
3. For all k+1 < i < N, yi+1 > yi

Output

Output should contain 48 lines in the format presented in a sample (exactly three digits after the decimal point should be printed).

Sample Input

1

3
10 20
0 0
20 0

Sample Output

00:00 0.000
00:30 0.209
01:00 0.421
01:30 0.635
02:00 0.851
02:30 1.070
03:00 1.292
03:30 1.516
04:00 1.743
04:30 1.972
05:00 2.205
05:30 2.441
06:00 2.679
06:30 2.922
07:00 3.167
07:30 3.417
08:00 3.670
08:30 3.927
09:00 4.189
09:30 4.454
10:00 4.725
10:30 5.000
11:00 5.280
11:30 5.566
12:00 5.858
12:30 6.156
13:00 6.460
13:30 6.771
14:00 7.090
14:30 7.417
15:00 7.753
15:30 8.098
16:00 8.453
16:30 8.820
17:00 9.199
17:30 9.592
18:00 10.000
18:30 10.426
19:00 10.871
19:30 11.340
20:00 11.835
20:30 12.362
21:00 12.929
21:30 13.545
22:00 14.226
22:30 15.000
23:00 15.918
23:30 17.113

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