Problem: Vasya has an array a_1, a_2, ..., a_n.

You don't know this array, but he told you m facts about this array. The i-th fact is a triple of numbers t_i, l_i and r_i (0 ≤ t_i ≤ 1, 1 ≤ l_i < r_i ≤ n) and it means:

  * if t_i=1 then subbarray a_{l_i}, a_{l_i + 1}, ..., a_{r_i} is sorted in non-decreasing order; 
  * if t_i=0 then subbarray a_{l_i}, a_{l_i + 1}, ..., a_{r_i} is not sorted in non-decreasing order. A subarray is not sorted if there is at least one pair of consecutive elements in this subarray such that the former is greater than the latter. 



For example if a = [2, 1, 1, 3, 2] then he could give you three facts: t_1=1, l_1=2, r_1=4 (the subarray [a_2, a_3, a_4] = [1, 1, 3] is sorted), t_2=0, l_2=4, r_2=5 (the subarray [a_4, a_5] = [3, 2] is not sorted), and t_3=0, l_3=3, r_3=5 (the subarray [a_3, a_5] = [1, 3, 2] is not sorted).

You don't know the array a. Find any array which satisfies all the given facts.

Input

The first line contains two integers n and m (2 ≤ n ≤ 1000, 1 ≤ m ≤ 1000).

Each of the next m lines contains three integers t_i, l_i and r_i (0 ≤ t_i ≤ 1, 1 ≤ l_i < r_i ≤ n).

If t_i = 1 then subbarray a_{l_i}, a_{l_i + 1}, ... , a_{r_i} is sorted. Otherwise (if t_i = 0) subbarray a_{l_i}, a_{l_i + 1}, ... , a_{r_i} is not sorted.

Output

If there is no array that satisfies these facts in only line print NO (in any letter case).

If there is a solution, print YES (in any letter case). In second line print n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the array a, satisfying all the given facts. If there are multiple satisfying arrays you can print any of them.

Examples

Input


7 4
1 1 3
1 2 5
0 5 6
1 6 7


Output


YES
1 2 2 3 5 4 4


Input


4 2
1 1 4
0 2 3


Output


NO

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
template <class T, class U>
inline void add_self(T &a, U b) {
  a += b;
  if (a >= mod) a -= mod;
  if (a < 0) a += mod;
}
template <class T, class U>
inline void min_self(T &x, U y) {
  if (y < x) x = y;
}
template <class T, class U>
inline void max_self(T &x, U y) {
  if (y > x) x = y;
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  cout << t;
  ;
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
template <class T, class U>
void print_m(const map<T, U> &m, int w = 3) {
  if (m.empty()) {
    cout << "Empty" << endl;
    return;
  }
  for (auto x : m) cout << "(" << x.first << ": " << x.second << ")," << endl;
  cout << endl;
}
template <class T, class U>
void debp(const pair<T, U> &pr, bool end_line = 1) {
  cout << "{" << pr.first << " " << pr.second << "}";
  cout << (end_line ? "\n" : ", ");
}
template <class T>
void print_vp(const T &vp, int sep_line = 0) {
  if (vp.empty()) {
    cout << "Empty" << endl;
    return;
  }
  if (!sep_line) cout << "{ ";
  for (auto x : vp) debp(x, sep_line);
  if (!sep_line) cout << "}\n";
  cout << endl;
}
template <typename T>
void print(const T &v, bool show_index = false) {
  int w = 2;
  if (show_index) {
    for (int i = 0; i < int((v).size()); i++) cout << setw(w) << i << " ";
    cout << endl;
  }
  for (auto &el : v) cout << setw(w) << el << " ";
  cout << endl;
}
template <typename T>
void print_vv(const T &vv) {
  if (int((vv).size()) == 0) {
    cout << "Empty" << endl;
    return;
  }
  int w = 3;
  cout << setw(w) << " ";
  for (int j = 0; j < int((*vv.begin()).size()); j++)
    cout << setw(w) << j << " ";
  cout << endl;
  int i = 0;
  for (auto &v : vv) {
    cout << i++ << " {";
    for (auto &el : v) cout << setw(w) << el << " ";
    cout << "},\n";
  }
  cout << endl;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, m;
  while (cin >> n >> m) {
    vector<pair<int, int> > bad;
    vector<int> ans(n + 2, -1);
    for (int i = 0; i < int(m); i++) {
      int t;
      pair<int, int> p;
      cin >> t >> p.first >> p.second;
      if (t) {
        for (int i = p.first + 1; i <= p.second; ++i) {
          ans[i] = 0;
        }
      } else {
        bad.push_back(p);
      }
    }
    bool ok = true;
    for (auto p : bad) {
      bool f = 0;
      for (int i = p.first + 1; i <= p.second; ++i) {
        if (ans[i] == -1) f = 1;
      }
      if (!f) ok = 0;
    }
    if (!ok) {
      cout << "NO\n";
      continue;
    }
    cout << "YES\n";
    ans[0] = n + 10;
    for (int i = 1; i <= n; ++i) {
      ans[i] += ans[i - 1];
    }
    for (int i = int(1); i < int(n + 1); i++) cout << ans[i] << " ";
    cout << "\n";
  }
  return 0;
}