main = -> { n, m = read_line.split.map &.to_i64 graph = NgLib::BfsGraph.new(3 * n) graph2 = NgLib::BfsGraph.new(3 * n) m.times do u, v = read_line.split.map &.to_i64.pred graph.add_edge(u, v, directed: true) graph.add_edge(u + n, v + n, directed: true) graph.add_edge(u + 2*n, v + 2*n, directed: true) graph2.add_edge(u, v, directed: true) graph2.add_edge(u + n, v + n, directed: true) graph2.add_edge(u + 2*n, v + 2*n, directed: true) end graph.add_edge(n - 2, n - 2 + n, directed: true) graph.add_edge(n - 1 + n, n - 1 + 2*n, directed: true) graph2.add_edge(n - 1, n - 1 + n, directed: true) graph2.add_edge(n - 2 + n, n - 2 + 2*n, directed: true) d = Math.min(graph.shortest_path(0, 0 + 2*n), graph2.shortest_path(0, 0 + 2*n)) puts d >= OO ? -1 : d - 2 } main.call OO = (1_i64 << 62) - (1_i64 << 31) module NgLib # $n$ 頂点 $m$ 辺からなるグラフに対して、幅優先探索によって最短経路を求めます。 # # 経路の復元も可能です。 class BfsGraph getter size : Int32 getter graph : Array(Array(Int32)) # $n$ 頂点 $0$ 辺からなるグラフを作成します。 # # ``` # graph = BfsGraph.new(n) # ``` def initialize(n : Int) @size = n.to_i64.to_i32 @graph = Array.new(@size) { Array(Int32).new } end # 辺 $(u, v)$ を追加します。 # # `directed` が `true` の場合、 # 有向辺とみなして、$u$ から $v$ への辺のみ生やします。 # # ``` # graph = BfsGraph.new(n) # graph.add_edge(u, v) # => (u) <---w---> (v) # graph.add_edge(u, v, directed: true) # => (u) ----w---> (v) # ``` def add_edge(u : Int, v : Int, directed : Bool = false) @graph[u.to_i32] << v.to_i32 @graph[v.to_i32] << u.to_i32 unless directed end # 全点対間の最短経路長を返します。 # # ``` # dists = graph.shortest_path # dists # => [[0, 1, 3], [1, 0, 2], [1, 1, 0]] # ``` def shortest_path (0...@size).map { |s| shortest_path(s) } end # 始点 `start` から各頂点への最短経路長を返します。 # # ``` # dist = graph.shortest_path(start: 2) # dist # => [3, 8, 0, 7, 1] # ``` def shortest_path(start : Int) queue = Deque.new([start.to_i32]) dist = Array.new(@size) { |i| i == start ? 0_i64 : OO } until queue.empty? from = queue.shift @graph[from].each do |to| next if dist[to] != OO dist[to] = dist[from] + 1 queue << to end end dist end # 始点 `start` から終点 `dest` への最短経路長を返します。 # # ``` # dist = graph.shortest_path(start: 2, dest: 0) # dist # => 12 # ``` def shortest_path(start : Int, dest : Int) shortest_path(start)[dest] end end end