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 Lua (LuaJIT 2.1.0) (judge verdict: Wrong Answer)

local mmi, mma = math.min, math.max
local bls, brs = bit.lshift, bit.rshift
local bxor = bit.bxor

local function grayCode(x)
  return bxor(x, brs(x, 1))
end

-- add_func(idx), rm_func(idx), work_func()
local function grayWalk(size, add_func, rm_func, work_func)
  local prv = 0
  local total = bls(1, size) - 1
  local bpos = {}
  for i = 1, size do
    bpos[bls(1, i - 1)] = i
  end
  work_func()
  for i = 1, total do
    local v = grayCode(i)
    if prv < v then
      prv, v = v, v - prv
      add_func(bpos[v])
    else
      prv, v = v, prv - v
      rm_func(bpos[v])
    end
    work_func()
  end
end

local n = io.read("*n")
local t = {}
local maps = {}
for i = 1, n do
  t[i] = 0
  local a = io.read("*n")
  maps[i] = {}
  for j = 1, a do
    local p, q = io.read("*n", "*n")
    maps[i][p] = q
  end
end

local function add_func(idx)
  t[idx] = 1
end
local function rm_func(idx)
  t[idx] = 0
end
local ret = 0
local function work_func()
  local valid = true
  local c = 0
  for i = 1, n do
    if t[i] == 1 then
      c = c + 1
      for k, v in pairs(maps[i]) do
        if t[k] ~= v then
          valid = false break
        end
      end
    else
      for k, v in pairs(maps[i]) do
        if t[k] == v then
          valid = false break
        end
      end
    end
    if not valid then break end
  end
  if valid then
    ret = mma(ret, c)
  end
end

grayWalk(n, add_func, rm_func, work_func)
print(ret)