Problem: Pavel is going to make a game of his dream. However, he knows that he can't make it on his own so he founded a development company and hired n workers of staff. Now he wants to pick n workers from the staff who will be directly responsible for developing a game.

Each worker has a certain skill level vi. Besides, each worker doesn't want to work with the one whose skill is very different. In other words, the i-th worker won't work with those whose skill is less than li, and with those whose skill is more than ri.

Pavel understands that the game of his dream isn't too hard to develop, so the worker with any skill will be equally useful. That's why he wants to pick a team of the maximum possible size. Help him pick such team.

Input

The first line contains a single integer n (1 ≤ n ≤ 105) — the number of workers Pavel hired.

Each of the following n lines contains three space-separated integers li, vi, ri (1 ≤ li ≤ vi ≤ ri ≤ 3·105) — the minimum skill value of the workers that the i-th worker can work with, the i-th worker's skill and the maximum skill value of the workers that the i-th worker can work with.

Output

In the first line print a single integer m — the number of workers Pavel must pick for developing the game.

In the next line print m space-separated integers — the numbers of the workers in any order.

If there are multiple optimal solutions, print any of them.

Examples

Input

4
2 8 9
1 4 7
3 6 8
5 8 10


Output

3
1 3 4


Input

6
3 5 16
1 6 11
4 8 12
7 9 16
2 10 14
8 13 15


Output

4
1 2 3 5

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
std::istream& operator>>(std::istream& i, pair<T, U>& p) {
  i >> p.first >> p.second;
  return i;
}
template <typename T>
std::istream& operator>>(std::istream& i, vector<T>& t) {
  for (auto& v : t) {
    i >> v;
  }
  return i;
}
template <typename T, typename U>
std::ostream& operator<<(std::ostream& o, const pair<T, U>& p) {
  o << p.first << ' ' << p.second;
  return o;
}
template <typename T>
std::ostream& operator<<(std::ostream& o, const vector<T>& t) {
  if (t.empty()) o << '\n';
  for (size_t i = 0; i < t.size(); ++i) {
    o << t[i] << " \n"[i == t.size() - 1];
  }
  return o;
}
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T, vector<T>, less<T>>;
template <typename T>
bool in(T a, T b, T c) {
  return a <= b && b < c;
}
unsigned int logceil(int first) {
  return 8 * sizeof(int) - __builtin_clz(first);
}
namespace std {
template <typename T, typename U>
struct hash<pair<T, U>> {
  hash<T> t;
  hash<U> u;
  size_t operator()(const pair<T, U>& p) const {
    return t(p.first) ^ (u(p.second) << 7);
  }
};
}  // namespace std
template <typename T, typename F>
T bsh(T l, T h, const F& f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      l = m + 1;
      r = m;
    } else {
      h = m - 1;
    }
  }
  return r;
}
template <typename F>
double bshd(double l, double h, const F& f, double p = 1e-9) {
  unsigned int r = 3 + (unsigned int)log2((h - l) / p);
  while (r--) {
    double m = (l + h) / 2;
    if (f(m)) {
      l = m;
    } else {
      h = m;
    }
  }
  return (l + h) / 2;
}
template <typename T, typename F>
T bsl(T l, T h, const F& f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      h = m - 1;
      r = m;
    } else {
      l = m + 1;
    }
  }
  return r;
}
template <typename F>
double bsld(double l, double h, const F& f, double p = 1e-9) {
  unsigned int r = 3 + (unsigned int)log2((h - l) / p);
  while (r--) {
    double m = (l + h) / 2;
    if (f(m)) {
      h = m;
    } else {
      l = m;
    }
  }
  return (l + h) / 2;
}
template <typename T>
T gcd(T a, T b) {
  if (a < b) swap(a, b);
  return b ? gcd(b, a % b) : a;
}
template <typename T>
class vector2 : public vector<vector<T>> {
 public:
  vector2() {}
  vector2(size_t a, size_t b, T t = T())
      : vector<vector<T>>(a, vector<T>(b, t)) {}
};
template <typename T>
class vector3 : public vector<vector2<T>> {
 public:
  vector3() {}
  vector3(size_t a, size_t b, size_t c, T t = T())
      : vector<vector2<T>>(a, vector2<T>(b, c, t)) {}
};
template <typename T>
class vector4 : public vector<vector3<T>> {
 public:
  vector4() {}
  vector4(size_t a, size_t b, size_t c, size_t d, T t = T())
      : vector<vector3<T>>(a, vector3<T>(b, c, d, t)) {}
};
template <typename T>
class vector5 : public vector<vector4<T>> {
 public:
  vector5() {}
  vector5(size_t a, size_t b, size_t c, size_t d, size_t e, T t = T())
      : vector<vector4<T>>(a, vector4<T>(b, c, d, e, t)) {}
};
template <typename F>
struct NoOp {
  void setup(unsigned int) {}
  void op(F& p, F n, unsigned int, unsigned int) { p = n; }
  void down(F&, F&, F&, unsigned int, unsigned int) {}
};
template <typename F, typename SetOp, typename PowerOp>
struct Lazy {
  void setup(unsigned int s) {
    this->s = s;
    L = new F[s]();
  }
  void down(F& u, F& l, F& r, unsigned int i, unsigned int s) {
    op(l, L[i], i << 1, s >> 1);
    op(r, L[i], i << 1 | 1, s >> 1);
    L[i] = 0;
  }
  void op(F& p, F n, unsigned int i, unsigned int s) {
    p = sop(p, pop(n, s));
    if (i < this->s) this->L[i] = sop(this->L[i], n);
  }
  SetOp sop;
  PowerOp pop;
  F* L;
  unsigned int s;
};
template <typename F, typename CombineOp, typename ModifyOp = NoOp<F>>
struct SegTree {
  void setup(unsigned int s, F def) {
    n = 1 << logceil(s);
    T = vector<F>(2 * n, def);
    for (unsigned int i = n - 1; i > 0; i--)
      T[i] = cop(T[i << 1], T[i << 1 | 1]);
    mop.setup(2 * n);
  }
  void setup(vector<F>& data, F def = F()) {
    n = 1 << logceil(data.size());
    T = vector<F>(2 * n, def);
    copy(data.begin(), data.end(), T.begin() + n);
    for (unsigned int i = n - 1; i > 0; i--)
      T[i] = cop(T[i << 1], T[i << 1 | 1]);
    mop.setup(2 * n);
  }
  inline void put(unsigned int first, F n) { put(first, first, n); }
  inline void put(unsigned int from, unsigned int to, F v) {
    put2(from, to + 1, v, 1, n);
  }
  inline F get(unsigned int first) { return get(first, first); }
  inline F get(unsigned int from, unsigned int to) {
    return get2(from, to + 1, 1, n);
  }
  void put2(unsigned int from, unsigned int to, F v, unsigned int i,
            unsigned int s) {
    if (from == 0 && to == s) {
      mop.op(T[i], v, i, s);
      return;
    }
    mop.down(T[i], T[i << 1], T[i << 1 | 1], i, s);
    s >>= 1;
    i <<= 1;
    if (to <= s) {
      put2(from, to, v, i, s);
    } else if (from >= s) {
      put2(from - s, to - s, v, i | 1, s);
    } else {
      put2(from, s, v, i, s);
      put2(0, to - s, v, i | 1, s);
    }
    T[i >> 1] = cop(T[i], T[i | 1]);
  }
  F get2(unsigned int from, unsigned int to, unsigned int i, unsigned int s) {
    while (true) {
      if (from == 0 && to == s) return T[i];
      mop.down(T[i], T[i << 1], T[i << 1 | 1], i, s);
      s >>= 1;
      i <<= 1;
      if (to > s) {
        to -= s;
        if (from >= s) {
          from -= s;
          i |= 1;
        } else
          return cop(get2(from, s, i, s), get2(0, to, i | 1, s));
      }
    }
  }
  unsigned int n;
  vector<F> T;
  CombineOp cop;
  ModifyOp mop;
};
template <typename F>
struct AddOp {
  F operator()(F a, F b) { return a + b; }
};
template <typename F>
struct MinOp {
  F operator()(F a, F b) { return std::min(a, b); }
};
template <typename F>
struct MaxOp {
  F operator()(F a, F b) { return std::max(a, b); }
};
template <typename F>
struct MultiplyOp {
  F operator()(F a, F b) { return a * b; }
};
template <typename F>
struct MultOp {
  F operator()(F a, unsigned int b) { return a * b; }
};
template <typename F>
struct IdempOp {
  F operator()(F a, unsigned int b) { return a; }
};
template <typename F>
struct InverseOp {
  F operator()(F a, F b) { return b ? b - a : a; }
};
template <typename T>
using AddSumTree = SegTree<T, AddOp<T>, Lazy<T, AddOp<T>, MultOp<T>>>;
template <typename T>
using AddMaxTree = SegTree<T, MaxOp<T>, Lazy<T, AddOp<T>, IdempOp<T>>>;
template <typename T>
using AddMinTree = SegTree<T, MinOp<T>, Lazy<T, AddOp<T>, IdempOp<T>>>;
template <typename T>
using AssignMinTree = SegTree<T, MinOp<T>, Lazy<T, MinOp<T>, IdempOp<T>>>;
template <typename T>
using AssignMaxTree = SegTree<T, MaxOp<T>, Lazy<T, MaxOp<T>, IdempOp<T>>>;
template <typename T>
using XorTree = SegTree<T, AddOp<T>, Lazy<T, InverseOp<T>, MultOp<T>>>;
template <typename T>
using SetMinTree = SegTree<T, MinOp<T>>;
template <typename T>
using SetMaxTree = SegTree<T, MaxOp<T>>;
template <typename T>
using SetMulTree = SegTree<T, MultiplyOp<T>>;
class developinggame {
 public:
  void solve(istream& cin, ostream& cout) {
    int N;
    cin >> N;
    vector<pair<int, std::pair<int, int>>> P(N);
    cin >> P;
    vector<vector<int>> In(3e5 + 1), Out(3e5 + 1);
    for (int i = 0; i < N; ++i) {
      In[P[i].first].push_back(i);
      Out[P[i].second.first].push_back(i);
    }
    AddMaxTree<int> A;
    A.setup(3e5 + 1, 0);
    std::pair<int, int> best{-1, 0};
    for (int i = 1; i <= 3e5; ++i) {
      for (int j : In[i]) A.put(P[j].second.first, P[j].second.second, 1);
      int g = A.get(0, 3e5);
      best = max(best, {g, i});
      for (int j : Out[i]) A.put(P[j].second.first, P[j].second.second, -1);
    }
    int l = best.second;
    vector<int> X(3e5 + 2, 0);
    for (auto& p : P) {
      if (p.first <= l && p.second.first >= l) {
        X[p.second.first]++;
        X[p.second.second + 1]--;
      }
    }
    std::pair<int, int> ans{-1, 0};
    for (int i = 1; i <= 3e5; ++i) {
      X[i] += X[i - 1];
      ans = max(ans, {X[i], i});
    }
    int first = ans.second;
    vector<int> Ans;
    for (int i = 0; i < N; ++i) {
      auto& p = P[i];
      if (p.first <= l && p.second.first >= l && p.second.first <= first &&
          p.second.second >= first) {
        Ans.push_back(i + 1);
      }
    }
    cout << best.first << '\n' << Ans;
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  developinggame solver;
  std::istream& in(std::cin);
  std::ostream& out(std::cout);
  solver.solve(in, out);
  return 0;
}