Problem:
Score : 300 points

Problem Statement

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}

Output

Print the maximum possible number of honest persons among the N people.

Sample Input 1

3
1
2 1
1
1 1
1
2 0

Sample 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.

Sample Input 2

3
2
2 1
3 0
2
3 1
1 0
2
1 1
2 0

Sample Output 2

0

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

Sample Input 3

2
1
2 0
1
1 0

Sample Output 3

1

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(input) {
  const lines = input.split("\n");
  const n = +lines[0];
  const rest = lines.slice(1);

  /**
   * 証言一覧
   * @type {[xij, yij][]}
   */
  const rules = [];
  var ai, rule;
  var i, j;
  for (i = 0; i < rest.length; i++) {
    ai = +rest[i];
    rule = [];
    for (j = 1; j <= ai; j++) {
      rule.push(rest[i + j].split(' ').map(Number));
    }
    rules.push(rule);
    i += ai;
  }

  var answer = 0, honestFlags, honestsCount;
  // bit全探索
  for (honestFlags = Math.pow(2, n) - 1; honestFlags > 0; honestFlags--) {
    honestsCount = countHonests(honestFlags);

    // 正直者の数がこれまでの最大値以下なら検証しない
    if (honestsCount <= answer) {
      continue;
    }

    // 矛盾がないかどうか確認
    if (checkIsValid(honestFlags, rules)) {
      answer = honestsCount;
    }
  }

  //出力
  console.log(answer);
}

/**
 * ビットフラグ中の正直者の数をカウント
 * @param {number} honestFlags 正直者ビットフラグ
 */
function countHonests(honestFlags) {
  var tmpHonestFlags = honestFlags;
  var count = 0;
  while (tmpHonestFlags > 0) {
    if (tmpHonestFlags % 2) {
      count++;
    }
    tmpHonestFlags = tmpHonestFlags >> 1;
  }

  return count;
}

/**
 * 証言に矛盾がないかどうか検証
 * @param {number} honestFlags 正直者ビットフラグ
 * @param rules 証言一覧
 */
function checkIsValid(honestFlags, rules) {
  return rules.every((rule, i) => {
    // 証言者が正直者かどうか
    const isHonest = (honestFlags >> i) % 2;
    // 正直者でなければ検証しない
    if (!isHonest) {
      return true;
    }

    // i人目の証言に矛盾がないか確認
    return rule.every((r) => {
      const xij = r[0];
      // xij人目が正直者かどうか(証言)
      const yij = r[1];
      // xij人目が正直者かどうか(実際)
      const xijIsHonest = (honestFlags >> (xij - 1)) % 2;

      return yij === xijIsHonest;
    });
  });
}

Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());