// O(n)
void bfs(int u,   vector<vector<int>>& g, vector<int>& vis){
    queue<int> q;
    q.push(u);
    while(!q.empty()){
        int v = q.front();
        vis[v] = 1;
        q.pop();
        for(int ch: g[v]){
           q.push(ch);
        }
    }
 }

// determine whether there are players whose rank is certain
bool toposort(int n, vector<vector<int>>& g, vector<vector<int>>& g_inv){
  vector<int> indegree(n+1,0);
   for(auto& it: g){
      for(int children: it){
         indegree[children]++;
      }
   }
   // [1,2,3,4,5]
   // [0,3,1,0,1]
   queue<int> q;
    vector<int> tp;
  // o(n)
   for(int i=1;i<=n;i++){
      if(indegree[i]==0){
          q.push(i);
      }
   }
  // O(n)
    while(!q.empty())}{
      int player = q.front();
      q.pop();
      tp.push_back(player);
      for(auto& ch: g[player]){
          indegree[ch]--;
          if(indegree[ch]==0)
              q.push(ch);
      }
}
    int last = tp[n-1];
    vector<int> vis(n+1,0);
    bfs(last,g_inv,vis);

  // o(n)
    for(int i=1;i<=n;i++){
        if(vis[i]==0){
            return false;
        }
    }
     return true;
 }



 }

bool game(int n, vector<vector<int>>& results) {
  vector<vector<int>> g(n+1);
  for(auto& it: results){
      int winner = it[0];
    int loser = it[1];
    g[winner].push_back(loser);
    ginv[loser].push_back(winner);
  }
   return toposort(n,g, g_inv);
}