# require "template" lib C fun strtoll(s : UInt8*, p : UInt8**, b : Int32) : Int64 end class String def to_i64 C.strtoll(self, nil, 10) end end # require "graph/bipartite_matching" # require "./graph" struct Edge(T) property to : Int32 property cost : T def initialize(@to : Int32, @cost : T) end def to_s(io) : Nil io << {to, cost} end def inspect(io) : Nil io << "->#{to}(#{cost})" end end struct Edge2(T) property from : Int32 property to : Int32 property cost : T def initialize(@from : Int32, @to : Int32, @cost : T) end def reverse Edge2(T).new(to, from, cost) end def to_s(io) : Nil io << {from, to, cost} end def inspect(io) : Nil io << "#{from}->#{to}(#{cost})" end end class Graph(T) getter size : Int32 getter graph : Array(Array(Edge(T))) def initialize(@size : Int32) raise ArgumentError.new("Negative graph size: #{size}") unless size >= 0 @graph = Array.new(size) { Array(Edge(T)).new } end def initialize(@size, edges : Array(Edge2(T)), undirected : Bool) raise ArgumentError.new("Negative graph size: #{size}") unless size >= 0 @graph = Array.new(size) { Array(Edge(T)).new } edges.each do |edge| @graph[edge.from] << Edge.new(edge.to, edge.cost) @graph[edge.to] << Edge.new(edge.from, edge.cost) if undirected end end def add_edge(i : Int32, j : Int32, cost : T) raise IndexError.new unless 0 <= i < size raise IndexError.new unless 0 <= j < size graph[i] << Edge(T).new(j, cost) graph[j] << Edge(T).new(i, cost) end def add_edge_directed(i : Int32, j : Int32, cost : T) raise IndexError.new unless 0 <= i < size raise IndexError.new unless 0 <= j < size graph[i] << Edge(T).new(j, cost) end def [](i : Int32) graph[i] end def each_edge : Nil (0...size).each do |v| graph[v].each do |edge| yield Edge2(T).new(v, edge.to, edge.cost) end end end def edges : Array(Edge2(T)) result = [] of Edge2(T) each_edge do |edge| result << edge end result end end class BipartiteMatching getter left : Int32 getter right : Int32 getter graph : Graph(Nil) def initialize(@left, @right) raise ArgumentError.new "Negative left vertexes size: #{left}" unless left >= 0 raise ArgumentError.new "Negative right vertexes size: #{right}" unless right >= 0 @graph = Graph(Nil).new(left) @left_match = Array(Int32?).new(left, nil) @right_match = Array(Int32?).new(right, nil) @used = Array(Bool).new(left, false) end def add_edge(l : Int32, r : Int32) raise IndexError.new unless 0 <= l < left raise IndexError.new unless 0 <= r < right graph[l] << Edge.new(r, nil) self end def add_edge(edges : Array(Edge2(Nil))) edges.each do |edge| add_edge(edge.from, edge.to) end self end private def dfs(v : Int32) : Bool return false if @used[v] @used[v] = true graph[v].each do |edge| if @right_match[edge.to].nil? || dfs(@right_match[edge.to].not_nil!) @left_match[v], @right_match[edge.to] = edge.to, v return true end end return false end def solve : Int32 while (0...left).reduce(false) { |update, i| update | (@left_match[i].nil? ? dfs(i) : false) } @used.fill(false) end left - @left_match.count(&.nil?) end end h, w = read_line.split.map(&.to_i) a = (1..h).map { read_line.split.map(&.to_i) } l, r = 0, 0 edges = Array.product((0...h).to_a, (0...w).to_a).group_by { |(i, j)| a[i][j] }.flat_map { |val, points| next [] of Edge2(Nil) if val == 0 row = {} of Int32 => Int32 column = {} of Int32 => Int32 points.map do |(y, x)| ll = row[y]? || (row[y] = (l += 1) - 1) rr = column[x]? || (column[x] = (r += 1) - 1) Edge2.new(ll, rr, nil) end } puts BipartiteMatching.new(l, r).add_edge(edges).solve