{"raw_statement":[{"iden":"statement","content":"Diego knows that the sum of all integers between $1$ and $N$ is $frac(N (N + 1), 2)$. However, he is wondering how to compute the exclusive or of all integers between $1$ and $N$.\n\nExclusive or is also known as xor. Most programming languages represent it with the character _^_.\n\nFirst, a single integer, $T$ $(1 <= T <= 10^5)$: the number of test cases.\n\nThen $T$ lines, each of which contains a single integer, $N$ $(1 <= N <= 10^(18))$.\n\nFor each test case output a line containing a single integer: the exclusive or of every number between $1$ and $N$.\n\n"},{"iden":"input","content":"First, a single integer, $T$ $(1 <= T <= 10^5)$: the number of test cases.Then $T$ lines, each of which contains a single integer, $N$ $(1 <= N <= 10^(18))$."},{"iden":"output","content":"For each test case output a line containing a single integer: the exclusive or of every number between $1$ and $N$."}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ T \\in \\mathbb{Z} $ be the number of test cases.  \nFor each test case $ k \\in \\{1, \\dots, T\\} $, let $ N_k \\in \\mathbb{Z} $ be a positive integer.\n\n**Constraints**  \n1. $ 1 \\le T \\le 10^5 $  \n2. For each $ k $, $ 1 \\le N_k \\le 10^{18} $\n\n**Objective**  \nFor each test case $ k $, compute:  \n$$\nX_k = \\bigoplus_{i=1}^{N_k} i\n$$  \nwhere $ \\oplus $ denotes the bitwise XOR operation.","simple_statement":"Given T test cases, for each given N, compute the XOR of all integers from 1 to N.","has_page_source":false}