Distinct Total Scores

In the Blue Bridge Cup finals this year, there are 10 problems with scores given in order as \(5, 5, 10, 10, 15, 15, 20, 20, 25, 25\). A contestant, when attempting each problem, scores either the full marks for that problem or 0. The total score is computed simply as the sum over all the 10 problems, irrespective of which problem contributed which score.

Your task is to determine the number of different total scores that a contestant can achieve.

Note: For example, scoring 5 on the first problem and 0 on the rest, or scoring 5 on the second problem and 0 on the rest, both yield a total score of 5 and should be counted as the same outcome.

Hint: For each distinct score value, note that the two problems with the same score can contribute \(0\), \(\text{score}\) or \(2 \times \text{score}\) points. Combine these possibilities for all score groups and count the distinct sums. It turns out that every multiple of 5 from \(0\) to \(150\) is achievable, so there are \(31\) possible total scores.

inputFormat

There is no input for this problem.

outputFormat

Output a single integer representing the number of different total scores a contestant can achieve.

sample

N/A

31