{"problem":{"name":"Two Sequences","description":{"content":"You are given two integer sequences, each of length $N$: $a_1, ..., a_N$ and $b_1, ..., b_N$. There are $N^2$ ways to choose two integers $i$ and $j$ such that $1 \\leq i, j \\leq N$. For each of these ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc092_b"},"statements":[{"statement_type":"Markdown","content":"You are given two integer sequences, each of length $N$: $a_1, ..., a_N$ and $b_1, ..., b_N$.\nThere are $N^2$ ways to choose two integers $i$ and $j$ such that $1 \\leq i, j \\leq N$. For each of these $N^2$ pairs, we will compute $a_i + b_j$ and write it on a sheet of paper. That is, we will write $N^2$ integers in total.\nCompute the XOR of these $N^2$ integers.\n\nDefinition of XOR\n\nThe XOR of integers $c_1, c_2, ..., c_m$ is defined as follows:\n\n*   Let the XOR be $X$. In the binary representation of $X$, the digit in the $2^k$'s place ($0 \\leq k$; $k$ is an integer) is $1$ if there are an odd number of integers among $c_1, c_2, ...c_m$ whose binary representation has $1$ in the $2^k$'s place, and $0$ if that number is even.\n\nFor example, let us compute the XOR of $3$ and $5$. The binary representation of $3$ is $011$, and the binary representation of $5$ is $101$, thus the XOR has the binary representation $110$, that is, the XOR is $6$.\n\n## Constraints\n\n*   All input values are integers.\n*   $1 \\leq N \\leq 200,000$\n*   $0 \\leq a_i, b_i < 2^{28}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$a_1$ $a_2$ $...$ $a_N$\n$b_1$ $b_2$ $...$ $b_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc092_b","tags":[],"sample_group":[["2\n1 2\n3 4","2\n\nOn the sheet, the following four integers will be written: $4(1+3), 5(1+4), 5(2+3)$ and $6(2+4)$."],["6\n4 6 0 0 3 3\n0 5 6 5 0 3","8"],["5\n1 2 3 4 5\n1 2 3 4 5","2"],["1\n0\n0","0"]],"created_at":"2026-03-03 11:01:14"}}