{"raw_statement":[{"iden":"statement","content":"You're given an array a with n elements. \n\nCompute the xor sum of the elements that appear an odd number of times in the array a.\n\nThe 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\n\nThe only line of the output contains the answer of the problem.\n\n"},{"iden":"input","content":"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"},{"iden":"output","content":"The only line of the output contains the answer of the problem."},{"iden":"examples","content":"Input54 4 3 3 4Output4"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ n \\in \\mathbb{Z} $ be the length of the array.  \nLet $ A = (a_1, a_2, \\dots, a_n) $ be a sequence of integers, where $ a_i \\in \\{0, 1, \\dots, 10^9\\} $.\n\nLet $ f(x) $ denote the frequency of element $ x $ in $ A $.\n\n**Constraints**  \n1. $ 1 \\leq n \\leq 3 \\times 10^6 $  \n2. $ 0 \\leq a_i \\leq 10^9 $ for all $ i \\in \\{1, \\dots, n\\} $\n\n**Objective**  \nCompute the XOR sum of all elements $ x $ such that $ f(x) $ is odd:  \n$$\n\\bigoplus_{\\substack{x \\in A \\\\ f(x) \\text{ odd}}} x\n$$","simple_statement":"Find the XOR of all numbers in the array that appear an odd number of times.","has_page_source":false}