#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


// |as| = n ==> |rs| = 2 n + 1
// [i - rs[i], i + rs[i]] is palindrome for $ as[0] $ as[1] $ ... $ as[n-1] $
// as[i, j): palindrome <=> j - i <= rs[i + j]
template <class String> vector<int> manacher(const String &as) {
  const int n = as.size();
  vector<int> rs(2 * n + 1);
  for (int i = 0, j = 0, k; i <= 2 * n; i += k, j -= k) {
    for (; 0 < i - j && i + j < 2 * n &&
           (!((i + j + 1) & 1) || as[(i - j - 1) >> 1] == as[(i + j + 1) >> 1]);
         ++j) {}
    rs[i] = j;
    for (k = 1; k < j && k + rs[i - k] < j; ++k) rs[i + k] = rs[i - k];
  }
  return rs;
}


/*
  when the direction is (1, 0), condition is:
  \sum[i] M[i] Y[i] ((t - X[i])^2 + Y[i])^(-3/2) = 0  for t >= 0
*/

constexpr Int L = 129600;

int N;
vector<Int> R, F, M;

int main() {
  for (; ~scanf("%d", &N); ) {
    R.resize(N);
    F.resize(N);
    M.resize(N);
    for (int u = 0; u < N; ++u) {
      scanf("%lld%lld%lld", &R[u], &F[u], &M[u]);
    }
    
    vector<Int> ans;
    if (N % 2 == 0) {
      vector<pair<Int, int>> fus(N);
      for (int u = 0; u < N; ++u) fus[u] = make_pair(F[u], u);
      sort(fus.begin(), fus.end());
      fus.emplace_back(fus[0]);
      fus.back().first += L;
      
      // (R, M) or (\delta F, 0)
      vector<pair<Int, Int>> ps(4*N);
      for (int i = 0; i < N; ++i) {
        const int u = fus[i].second;
        ps[i * 2 + 0] = ps[(N + i) * 2 + 0] = make_pair(R[u], M[u]);
        ps[i * 2 + 1] = ps[(N + i) * 2 + 1] = make_pair(fus[i + 1].first - fus[i].first, 0);
      }
      const auto rads = manacher(ps);
// cerr<<"ps = "<<ps<<", rads = "<<rads<<endl;
      
      /*
        cut between i-1 and i
        [i, i+N/2) vs [i+N/2, i+N)
      */
      for (int i = 1; i <= N; ++i) {
        const int l = i * 2 + 0;
        const int r = (i + N - 1) * 2 + 0 + 1;
        if (r - l <= rads[l + r]) {
          ans.push_back(fus[i - 1].first + fus[i].first);
        }
      }
    }
    
    printf("%d\n", (int)ans.size());
    for (const Int f : ans) {
      printf("%.1f\n", f / 2.0);
    }
  }
  return 0;
}