D. Xor Sum

Codeforces

IDCF10074D

Time1000ms

Memory4MB

Difficulty—

English · Original

Formal · Original

You're given an array a with n elements. Compute the xor sum of the elements that appear an odd number of times in the array a. The first line contains number n (1 ≤ n ≤ 3000000). The second line of the input contains n numbers, representing the array a. All elements of a are between 0 and 109 The only line of the output contains the answer of the problem. ## Input The first line contains number n (1 ≤ n ≤ 3000000). The second line of the input contains n numbers, representing the array a. All elements of a are between 0 and 109 ## Output The only line of the output contains the answer of the problem. [samples]

**Definitions** Let $ n \in \mathbb{Z} $ be the length of the array. Let $ A = (a_1, a_2, \dots, a_n) $ be a sequence of integers, where $ a_i \in \{0, 1, \dots, 10^9\} $. Let $ f(x) $ denote the frequency of element $ x $ in $ A $. **Constraints** 1. $ 1 \leq n \leq 3 \times 10^6 $ 2. $ 0 \leq a_i \leq 10^9 $ for all $ i \in \{1, \dots, n\} $ **Objective** Compute the XOR sum of all elements $ x $ such that $ f(x) $ is odd: $$ \bigoplus_{\substack{x \in A \\ f(x) \text{ odd}}} x $$

API Response (JSON)

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