XOR Circle

AtCoder

IDagc035_a

Time2000ms

Memory256MB

Difficulty—

Snuke has $N$ hats. The $i$\-th hat has an integer $a_i$ written on it. There are $N$ camels standing in a circle. Snuke will put one of his hats on each of these camels. If there exists a way to distribute the hats to the camels such that the following condition is satisfied for every camel, print `Yes`; otherwise, print `No`. * The bitwise XOR of the numbers written on the hats on both adjacent camels is equal to the number on the hat on itself. What is XOR? The bitwise XOR $x_1 \oplus x_2 \oplus \ldots \oplus x_n$ of $n$ non-negative integers $x_1, x_2, \ldots, x_n$ is defined as follows: - When $x_1 \oplus x_2 \oplus \ldots \oplus x_n$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if the number of integers among $x_1, x_2, \ldots, x_n$ whose binary representations have $1$ in the $2^k$'s place is odd, and $0$ if that count is even. For example, $3 \oplus 5 = 6$. ## Constraints * All values in input are integers. * $3 \leq N \leq 10^{5}$ * $0 \leq a_i \leq 10^{9}$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $\ldots$ $a_{N}$ [samples]

Samples

Input #1

3
1 2 3

Output #1

Yes

*   If we put the hats with $1$, $2$, and $3$ in this order, clockwise, the condition will be satisfied for every camel, so the answer is `Yes`.

Input #2

4
1 2 4 8

Output #2

No

*   There is no such way to distribute the hats; the answer is `No`.

API Response (JSON)

{
  "problem": {
    "name": "XOR Circle",
    "description": {
      "content": "Snuke has $N$ hats. The $i$\\-th hat has an integer $a_i$ written on it. There are $N$ camels standing in a circle. Snuke will put one of his hats on each of these camels. If there exists a way to dist",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc035_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has $N$ hats. The $i$\\-th hat has an integer $a_i$ written on it.\nThere are $N$ camels standing in a circle. Snuke will put one of his hats on each of these camels.\nIf there exists a way to dist...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments