HonestOrUnkind2

AtCoder

IDabc147_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ people numbered $1$ to $N$. Each of them is either an _honest_ person whose testimonies are always correct or an _unkind_ person whose testimonies may be correct or not. Person $i$ gives $A_i$ testimonies. The $j$\-th testimony by Person $i$ is represented by two integers $x_{ij}$ and $y_{ij}$. If $y_{ij} = 1$, the testimony says Person $x_{ij}$ is honest; if $y_{ij} = 0$, it says Person $x_{ij}$ is unkind. How many honest persons can be among those $N$ people at most? ## Constraints * All values in input are integers. * $1 \leq N \leq 15$ * $0 \leq A_i \leq N - 1$ * $1 \leq x_{ij} \leq N$ * $x_{ij} \neq i$ * $x_{ij_1} \neq x_{ij_2} (j_1 \neq j_2)$ * $y_{ij} = 0, 1$ ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $x_{11}$ $y_{11}$ $x_{12}$ $y_{12}$ $:$ $x_{1A_1}$ $y_{1A_1}$ $A_2$ $x_{21}$ $y_{21}$ $x_{22}$ $y_{22}$ $:$ $x_{2A_2}$ $y_{2A_2}$ $:$ $A_N$ $x_{N1}$ $y_{N1}$ $x_{N2}$ $y_{N2}$ $:$ $x_{NA_N}$ $y_{NA_N}$ [samples]

Samples

Input #1

Output #1

2

If Person $1$ and Person $2$ are honest and Person $3$ is unkind, we have two honest persons without inconsistencies, which is the maximum possible number of honest persons.

Input #2

Output #2

0

Assuming that one or more of them are honest immediately leads to a contradiction.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "HonestOrUnkind2",
    "description": {
      "content": "There are $N$ people numbered $1$ to $N$. Each of them is either an _honest_ person whose testimonies are always correct or an _unkind_ person whose testimonies may be correct or not. Person $i$ gives",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc147_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ people numbered $1$ to $N$. Each of them is either an _honest_ person whose testimonies are always correct or an _unkind_ person whose testimonies may be correct or not.\nPerson $i$ gives...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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