A. Olympiad

Codeforces

IDCF937A

Time1000ms

Memory256MB

Difficulty—

implementationsortings

English · Original

Chinese · Translation

Formal · Original

The recent All-Berland Olympiad in Informatics featured _n_ participants with each scoring a certain amount of points. As the head of the programming committee, you are to determine the set of participants to be awarded with diplomas with respect to the following criteria: * At least one participant should get a diploma. * None of those with score equal to zero should get awarded. * When someone is awarded, all participants with score **not less** than his score should also be awarded. Determine the number of ways to choose a subset of participants that will receive the diplomas. ## Input The first line contains a single integer _n_ (1 ≤ _n_ ≤ 100) — the number of participants. The next line contains a sequence of _n_ integers _a_1, _a_2, ..., _a__n_ (0 ≤ _a__i_ ≤ 600) — participants' scores. It's guaranteed that at least one participant has non-zero score. ## Output Print a single integer — the desired number of ways. [samples] ## Note There are three ways to choose a subset in sample case one. 1. Only participants with 3 points will get diplomas. 2. Participants with 2 or 3 points will get diplomas. 3. Everyone will get a diploma! The only option in sample case two is to award everyone. Note that in sample case three participants with zero scores cannot get anything.

最近的全俄罗斯信息学奥林匹克竞赛有 #cf_span[n] 名参赛者，每人获得一定的分数。作为编程委员会主席，你需要根据以下标准确定授予奖状的参赛者集合：计算选择获得奖状的参赛者子集的方式数。第一行包含一个整数 #cf_span[n] (#cf_span[1 ≤ n ≤ 100]) —— 参赛者人数。第二行包含一个包含 #cf_span[n] 个整数的序列 #cf_span[a1, a2, ..., an] (#cf_span[0 ≤ ai ≤ 600]) —— 参赛者的分数。保证至少有一名参赛者的分数非零。请输出一个整数 —— 所需的方式数。在第一个样例中，有三种选择子集的方式。第二个样例中唯一的选项是授予所有人。注意：在第三个样例中，分数为零的参赛者无法获得任何奖状。 ## Input 第一行包含一个整数 #cf_span[n] (#cf_span[1 ≤ n ≤ 100]) —— 参赛者人数。第二行包含一个包含 #cf_span[n] 个整数的序列 #cf_span[a1, a2, ..., an] (#cf_span[0 ≤ ai ≤ 600]) —— 参赛者的分数。保证至少有一名参赛者的分数非零。 ## Output 请输出一个整数 —— 所需的方式数。 [samples] ## Note 在第一个样例中，有三种选择子集的方式：仅授予得 3 分的参赛者；授予得 2 分或 3 分的参赛者；授予所有人。第二个样例中唯一的选项是授予所有人。注意：在第三个样例中，分数为零的参赛者无法获得任何奖状。

**Definitions** Let $ n \in \mathbb{Z} $ be the number of participants. Let $ A = (a_1, a_2, \dots, a_n) $ be a sequence of non-negative integers representing participants' scores, with $ \max(A) > 0 $. Let $ M = \max(A) $ be the maximum score. **Constraints** 1. $ 1 \leq n \leq 100 $ 2. $ 0 \leq a_i \leq 600 $ for all $ i \in \{1, \dots, n\} $ 3. $ M > 0 $ **Objective** Count the number of non-empty subsets $ S \subseteq \{1, \dots, n\} $ such that: $$ \forall i \in S,\ a_i = M $$ That is, only participants with the maximum score may be awarded, and at least one such participant must be selected. Let $ k = |\{ i \mid a_i = M \}| $. Then the number of valid subsets is: $$ 2^k - 1 $$

Samples

Input #1

4
1 3 3 2

Output #1

Input #2

3
1 1 1

Output #2

Input #3

4
42 0 0 42

Output #3

API Response (JSON)

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    "name": "A. Olympiad",
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    "platform": "Codeforces",
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    "difficulty": "None",
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    "is_sync": true,
    "sync_url": null,
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