Two Sequences

AtCoder

IDarc092_b

Time3000ms

Memory256MB

Difficulty—

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 $N^2$ 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. Compute the XOR of these $N^2$ integers. Definition of XOR The XOR of integers $c_1, c_2, ..., c_m$ is defined as follows: * 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. For 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 $6$. ## Constraints * All input values are integers. * $1 \leq N \leq 200,000$ * $0 \leq a_i, b_i < 2^{28}$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $...$ $a_N$ $b_1$ $b_2$ $...$ $b_N$ [samples]

Samples

Input #1

2
1 2
3 4

Output #1

2

On the sheet, the following four integers will be written: $4(1+3), 5(1+4), 5(2+3)$ and $6(2+4)$.

Input #2

6
4 6 0 0 3 3
0 5 6 5 0 3

Output #2

Input #3

5
1 2 3 4 5
1 2 3 4 5

Output #3

Input #4

1
0
0

Output #4

API Response (JSON)

{
  "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 ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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