G. Magical Indices

Codeforces

IDCF10153G

Time3000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Alaa sometimes feels bored at work, so at such times she starts playing with a beautiful array a consisting of n integers a1, a2, ..., an. Alaa starts counting the number of magical indices in the array a. An index x is said to be magical if it satisfying the following rules: Can you help Alaa by counting the number of magical indices in the array a. The first line contains an integer T, where T is the number of test cases. The first line of each test case contains an integer n (1 ≤ n ≤ 106), where n is the size of the array a. The second line of each test case contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106), giving the array a. For each test case, print a single line containing the number of magical indices in the array a. As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use _scanf/printf_ instead of _cin/cout_ in C++, prefer to use _BufferedReader/PrintWriter_ instead of _Scanner/System.out_ in Java. ## Input The first line contains an integer T, where T is the number of test cases.The first line of each test case contains an integer n (1 ≤ n ≤ 106), where n is the size of the array a.The second line of each test case contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106), giving the array a. ## Output For each test case, print a single line containing the number of magical indices in the array a. [samples] ## Note As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use _scanf/printf_ instead of _cin/cout_ in C++, prefer to use _BufferedReader/PrintWriter_ instead of _Scanner/System.out_ in Java.

**Definitions** Let $ T \in \mathbb{Z} $ be the number of test cases. For each test case $ k \in \{1, \dots, T\} $: - Let $ n_k \in \mathbb{Z} $ denote the size of the array. - Let $ A_k = (a_{k,1}, a_{k,2}, \dots, a_{k,n_k}) $ be the array of integers. **Constraints** 1. $ 1 \le T \le 10^5 $ 2. For each $ k \in \{1, \dots, T\} $: - $ 1 \le n_k \le 10^6 $ - $ 1 \le a_{k,i} \le 10^6 $ for all $ i \in \{1, \dots, n_k\} $ **Objective** For each test case $ k $, count the number of indices $ x \in \{1, \dots, n_k\} $ such that: $$ a_{k,x} = \sum_{\substack{j=1 \\ j \ne x}}^{n_k} a_{k,j} $$

API Response (JSON)

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    "name": "G. Magical Indices",
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