XOR Replace

AtCoder

IDagc016_d

Time2000ms

Memory256MB

Difficulty—

There is a sequence of length $N$: $a = (a_1, a_2, ..., a_N)$. Here, each $a_i$ is a non-negative integer. Snuke can repeatedly perform the following operation: * Let the XOR of all the elements in $a$ be $x$. Select an integer $i$ ($1 ≤ i ≤ N$) and replace $a_i$ with $x$. Snuke's objective is to match $a$ with another sequence $b = (b_1, b_2, ..., b_N)$. Here, each $b_i$ is a non-negative integer. Determine whether the objective is achievable, and find the minimum necessary number of operations if the answer is positive. ## Constraints * $2 ≤ N ≤ 10^5$ * $a_i$ and $b_i$ are integers. * $0 ≤ a_i, b_i < 2^{30}$ ## 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

3
0 1 2
3 1 0

Output #1

2

At first, the XOR of all the elements of $a$ is $3$. If we replace $a_1$ with $3$, $a$ becomes $(3, 1, 2)$.
Now, the XOR of all the elements of $a$ is $0$. If we replace $a_3$ with $0$, $a$ becomes $(3, 1, 0)$, which matches $b$.

Input #2

3
0 1 2
0 1 2

Output #2

Input #3

2
1 1
0 0

Output #3

\-1

Input #4

4
0 1 2 3
1 0 3 2

Output #4

API Response (JSON)

{
  "problem": {
    "name": "XOR Replace",
    "description": {
      "content": "There is a sequence of length $N$: $a = (a_1, a_2, ..., a_N)$. Here, each $a_i$ is a non-negative integer. Snuke can repeatedly perform the following operation: *   Let the XOR of all the elements in",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc016_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a sequence of length $N$: $a = (a_1, a_2, ..., a_N)$. Here, each $a_i$ is a non-negative integer.\nSnuke can repeatedly perform the following operation:\n\n*   Let the XOR of all the elements in...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments