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;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n, m, t, l, r;
  pair<int, int> p;
  cin >> n >> m;
  vector<pair<int, int>> sorted;
  vector<pair<int, int>> unsorted;
  vector<pair<int, int>> newSorted;
  while (m--) {
    cin >> t >> l >> r;
    if (t)
      sorted.push_back({l, r});
    else
      unsorted.push_back({l, r});
  }
  sort(sorted.rbegin(), sorted.rend());
  while ((int)(sorted).size()) {
    p = sorted.back();
    sorted.pop_back();
    while ((int)(sorted).size() && sorted.back().first <= p.second) {
      p.second = max(p.second, sorted.back().second);
      sorted.pop_back();
    }
    newSorted.push_back(p);
  }
  int a[n + 1];
  int b[n];
  for (int i = 1; i < n; ++i) b[i] = -1;
  a[1] = 1e6;
  for (auto i : newSorted)
    for (int j = i.first; j < i.second; ++j) b[j] = 1;
  set<int> s;
  for (int i = 2; i <= n; ++i) a[i] = a[i - 1] + b[i - 1];
  for (int i = 1; i < n; ++i)
    if (a[i] >= a[i + 1]) s.insert(i);
  for (auto i : unsorted) {
    if (s.lower_bound(i.first) == s.end()) {
      cout << "NO";
      return 0;
    }
    if (*(s.lower_bound(i.first)) >= i.second) {
      cout << "NO";
      return 0;
    }
  }
  cout << "YES\n";
  for (int i = 1; i <= n; ++i) cout << a[i] << " ";
  return 0;
}