#!/usr/bin/env python3 import sys from collections import defaultdict class UnionFind(): def __init__(self, n): self.n = n self.group_num = n self.parents = [-1] * n """ 要素xの値を取得。""" def find(self, x): if self.parents[x] < 0: return x else: self.parents[x] = self.find(self.parents[x]) return self.parents[x] """ 2つの要素の併合。""" def union(self, x, y): x = self.find(x) y = self.find(y) if x == y: return if self.parents[x] > self.parents[y]: x, y = y, x self.parents[x] += self.parents[y] self.parents[y] = x self.group_num -= 1 return """ 要素xの属する集合の要素数を取得。""" def size(self, x): return -self.parents[self.find(x)] """ 2つの要素が同一の集合に属するか。""" def same(self, x, y): return self.find(x) == self.find(y) """ 要素xと同一の集合の要素を全取得。 計算量 : O(N) """ def members(self, x): root = self.find(x) return [i for i in range(self.n) if self.find(i) == root] """ 各集合の根を全取得。 計算量 : O(N) """ def roots(self): return [i for i, x in enumerate(self.parents) if x < 0] """ 集合の個数を取得。 v2 計算量 : O(1) """ def group_count_v2(self): return self.group_num """ 集合の個数を取得。 v1 計算量 : O(N) """ def group_count_v1(self): return len(self.roots()) """ 全集合の要素一覧を取得。 計算量 : O(N) """ def all_group_members(self): group_members = defaultdict(list) for member in range(self.n): group_members[self.find(member)].append(member) return group_members def __str__(self): return '\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items()) sys.setrecursionlimit(10 ** 9) class SCC(): def __init__(self, N: int): self.N = N # 頂点数 self.G = [[] for _ in range(self.N)] # 与えられたグラフ self.rG = [[] for _ in range(self.N)] # 全ての辺を逆向きにしたグラフ self.seen = [False] * self.N # 各ノードが訪問済みかどうかのフラグ self.lastOrder = [] # ノードの帰りがけ順(0-indexで採番) self.associationNodeNumWithSccGroupNum = [-1] * self.N # SCC後の対応表(indexがノード番号。値が0-indexで採番されたSCCのグループの順番。値が若いものから順にトポロジカルソートされている) self.topologicalSortedList = [] # SCC後のトポロジカルソート済みリスト self.sccNum = 0 # SCCの個数 兼 強連結成分の採番用カウンタ(0-indexで採番) # 辺の追加 def addEdge(self, fromNode: int, toNode: int): # グラフ構築 self.G[fromNode].append(toNode) # 逆向きグラフを別途構築 self.rG[toNode].append(fromNode) # DFS def _dfs(self, now: int): self.seen[now] = True for next in self.G[now]: if self.seen[next]: continue self._dfs(next) self.lastOrder.append(now) # 逆向きグラフの強連結成分チェック def _reverseDfs(self, now: int): self.seen[now] = True self.associationNodeNumWithSccGroupNum[now] = self.sccNum self.topologicalSortedList.append(now) for next in self.rG[now]: if self.seen[next]: continue self._reverseDfs(next) # 強連結成分分解SCC def build(self): # 帰りがけ順のナンバリングDFS for startNode in range(self.N): if self.seen[startNode]: continue self._dfs(startNode) # seenをリセット self.seen = [False] * self.N # 帰りがけ順の大きい方から順に強連結成分の判定DFS for node in self.lastOrder[::-1]: if self.seen[node]: continue self._reverseDfs(node) self.sccNum += 1 return self.associationNodeNumWithSccGroupNum # 2つのノードが強連結か。 def same(self, a: int, b: int): return self.associationNodeNumWithSccGroupNum[a] == self.associationNodeNumWithSccGroupNum[b] # 強連結成分SCCを全取得。 def getAllSccGroups(self): res = [[] for _ in range(self.sccNum)] for nodeNum, sccGroupNum in enumerate(self.associationNodeNumWithSccGroupNum): res[sccGroupNum].append(nodeNum) return res def main(): N, M = map(int, input().split()) uf = UnionFind(N) G = [[] for _ in range(N)] for _ in range(M): A, B = map(int, input().split()) G[A - 1].append(B - 1) uf.union(A - 1, B - 1) dags = uf.all_group_members() # print(dags) # print(G) ans = [] for d in dags.values(): compressed = {} compressed_to_row = [] for index, val in enumerate(sorted(list(set(d)))): compressed[val] = index compressed_to_row.append(val) # print(compressed) sc = SCC(len(d)) for i in d: for j in G[i]: sc.addEdge(compressed[i], compressed[j]) sc.build() for i in range(len(d) - 1): ans.append(f"{compressed_to_row[sc.topologicalSortedList[i]] + 1} {compressed_to_row[sc.topologicalSortedList[i + 1]] + 1}") print(len(ans)) print(*ans, sep="\n") return if __name__ == '__main__': main()