Problem D: Anne's Game |
Time Limit: 2 seconds |
Lily: "Chantarelle was part of my exotic phase." Buffy: "It's nice. It's a mushroom." Lily: "It is? That's really embarrassing." Buffy: "Well, it's an exotic mushroom, if that's any comfort." |
A little girl whose name is Anne Spetring likes to play the following game. She draws a circle on paper. Then she draws another one and connects it to the first cicrle by a line. Then she draws another and connects it to one of the first two circles by a line. She continues this way until she has n circles drawn and each one connected to one of the previously drawn circles. Her circles never intersect and lines never cross. Finally, she numbers the circles from 1 to n in some random order.
How many different pictures can she draw that contain exactly n circles? Two pictures are different if one of them has a line connecting circle number i to circle number j, and the other picture does not.
The first line of input gives the number of cases, N. N test cases follow. Each one is a line containing n (0<n<=100).
For each test case, output one line containing "Case #x:" followed by X, where X is the remainder after dividing the answer by 2000000011.
Sample input |
Sample output |
---|---|
3 1 2 3 |
Case #1: 1 Case #2: 1 Case #3: 3 |