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;
template <class T>
void read(T &x) {
  cin >> x;
}
template <class H, class T>
void read(pair<H, T> &p) {
  cin >> p.first >> p.second;
}
template <class T, size_t S>
void read(array<T, S> &a) {
  for (T &i : a) read(i);
}
template <class T>
void read(vector<T> &v) {
  for (T &i : v) read(i);
}
template <class H, class... T>
void read(H &h, T &...t) {
  read(h);
  read(t...);
}
template <class H, class T>
ostream &operator<<(ostream &o, pair<H, T> &p) {
  o << p.first << " " << p.second;
  return o;
}
template <class T, size_t S>
ostream &operator<<(ostream &o, array<T, S> &a) {
  string s;
  for (T i : a) o << s << i, s = " ";
  return o;
}
template <class T>
ostream &operator<<(ostream &o, vector<T> &v) {
  string s;
  for (T i : v) o << s << i, s = " ";
  return o;
}
template <class T>
void write(T x) {
  cout << x;
}
template <class H, class... T>
void write(const H &h, const T &...t) {
  write(h);
  write(t...);
}
void print() { write('\n'); }
template <class H, class... T>
void print(const H &h, const T &...t) {
  write(h);
  if (sizeof...(t)) write(' ');
  print(t...);
}
template <class T>
bool ckmin(T &a, const T b) {
  return (b < a) ? a = b, 1 : 0;
}
template <class T>
bool ckmax(T &a, const T b) {
  return (a < b) ? a = b, 1 : 0;
}
using ll = long long;
void solve() {
  int n, m;
  read(n, m);
  vector<array<int, 2>> srt, not_srt;
  while (m--) {
    int t, l, r;
    read(t, l, r), --l, --r;
    if (t)
      srt.push_back({l, r});
    else
      not_srt.push_back({l, r});
  }
  vector<bool> must_srt(n + 1);
  for (auto [l, r] : srt)
    for (int i = l; i < r; ++i) must_srt[i] = 1;
  for (auto [l, r] : not_srt) {
    bool f = 0;
    for (int i = l; i < r; ++i) f |= !must_srt[i];
    if (!f) return void(print("NO"));
  }
  print("YES");
  int cur = 5e5;
  write(cur);
  for (int i = 0; i < n - 1; ++i) {
    if (must_srt[i])
      write(' ', ++cur);
    else
      write(' ', --cur);
  }
  print();
}
int main() {
  cin.tie(0)->sync_with_stdio(0);
  solve();
}