p1959_Darts

Darts

Time Limit: 1000MSMemory Limit: 30000KTotal Submissions: 781Accepted: 418

Description

Background
Many nations (including Germany) have a strange tradition ofthrowing small arrows at round flat targets (usually, these smallarrows are called darts and so is the game).
In a darts game, the target consists of a flat circle which isdivided into slices and rings. The slices are numbered from 1 to 20 andthe rings are called double or treble ring (see Figure 5). The centerpart of the board is called the bull’s eye which is further subdividedinto an inner part (the real bull’s eye) and an outer part (called thebull, see Fig. 5).

Players take turns in throwing the darts at the board. Their scoredepends on the areas they hit with their darts. Hitting the 20 slice inthe double ring scores 2 * 20 = 40 points. Hitting the treble ringmultiplies the score by 3. The inner part of the bull’s eye counts 50,the outer part 25 points.
Every turn consists of 3 darts being thrown at the dartboard by aplayer and his score is the sum of the scores of all darts which hitthe dartboard in one of the numbered areas.
Problem
Your friends have played darts yesterday and from their match thescores are still on the blackboard in your room. From reading thescores, you would like to know, how the individual players threw theirdarts and where they could have hit the dartboard. You are to write aprogram which, given the score of a turn,reconstructs the number ofpossible distinct combinations of hits of the three darts on thedartboard ignoring the order in which the darts are thrown.
As an example, consider the overall score of 3 of a player. This could have happened as follows:

3 = 0 +    0 +    1*3    one dart hits slice 3

3 = 0 +    0 +    3*1    one dart hits slice 1 in treble ring

3 = 0 +    1*1 +  1*2    one dart hits slice 1 and one dart hits slice 2

3 = 0 +    1*1 +  2*1    one dart hits slice 1 and one dart hits slice 1 in double ring

3 = 1*1 +  1*1 +  1*1    all three darts hit slice 1

The resulting sum of possible distinct combinations is 5.
A more complex example is score 9:

9 = 0 +    0 +    1*9    one dart hits slice 9

9 = 0 +    0 +    3*3    one dart hits slice 3 in treble ring

9 = 0 +    1*1 +  1*8    one dart hits slice 1 and one dart hits slice 8

9 = 0 +    1*1 +  2*4    one dart hits slice 1 and one dart hits slice 4 in double ring

...

9 = 0 +    3*2 +  1*3    one dart hits slice 2 in treble ring and one dart hits slice 3

9 = 1*1 +  1*1 +  1*7    two darts hit slice 1 and one dart hits slice 7

...

9 = 2*1 +  3*1 +  2*2    one dart hits slice 1 in double ring, one dart hits slice 1 in treble ring and one dart hits slice 2 in double ring

9 = 1*3 +  1*3 +  1*3    three darts hit slice 3

9 = 1*3 +  1*3 +  3*1    two darts hit slice 3 and one dart hits slice 1 in treble ring

9 = 1*3 +  3*1 +  3*1    one dart hits slice 3 and two darts hit slice 1 in treble ring

9 = 3*1 +  3*1 +  3*1    three darts hit slice 1 in treble ring

What is the number of combinations? Write a program to find out.

Input

The first line contains the number of scenarios.
For each scenario, you are give a dart score as a single positive integer on a line by itself.

Output

Theoutput for every scenario begins with a line containing "Scenario #i:",where i is the number of the scenario starting at 1. Then print thenumber of possible dart score combinations on a line by itself.Finishthe output of every scenario with a blank line.

Sample Input

2
3
9

Sample Output

Scenario #1:
5

Scenario #2:
41

Source

TUD Programming Contest 2002, Darmstadt, Germany