Xor Battle

AtCoder

IDagc045_a

Time2000ms

Memory256MB

Difficulty—

There are two persons, numbered $0$ and $1$, and a variable $x$ whose initial value is $0$. The two persons now play a game. The game is played in $N$ rounds. The following should be done in the $i$\-th round ($1 \leq i \leq N$): * Person $S_i$ does one of the following: * Replace $x$ with $x \oplus A_i$, where $\oplus$ represents bitwise XOR. * Do nothing. Person $0$ aims to have $x=0$ at the end of the game, while Person $1$ aims to have $x \neq 0$ at the end of the game. Determine whether $x$ becomes $0$ at the end of the game when the two persons play optimally. Solve $T$ test cases for each input file. ## Constraints * $1 \leq T \leq 100$ * $1 \leq N \leq 200$ * $1 \leq A_i \leq 10^{18}$ * $S$ is a string of length $N$ consisting of `0` and `1`. * All numbers in input are integers. ## Input Input is given from Standard Input in the following format. The first line is as follows: $T$ Then, $T$ test cases follow. Each test case is given in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ $S$ [samples]

Samples

Input #1

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000

Output #1

1
0
0

In the first test case, if Person $1$ replaces $x$ with $0 \oplus 1=1$, we surely have $x \neq 0$ at the end of the game, regardless of the choice of Person $0$.
In the second test case, regardless of the choice of Person $1$, Person $0$ can make $x=0$ with a suitable choice.

API Response (JSON)

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    "name": "Xor Battle",
    "description": {
      "content": "There are two persons, numbered $0$ and $1$, and a variable $x$ whose initial value is $0$. The two persons now play a game. The game is played in $N$ rounds. The following should be done in the $i$\\-",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc045_a"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are two persons, numbered $0$ and $1$, and a variable $x$ whose initial value is $0$. The two persons now play a game. The game is played in $N$ rounds. The following should be done in the $i$\\-...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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