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 inf = 1e9 + 10;
vector<pair<int, int>> modify(vector<pair<int, int>> v) {
  sort(v.begin(), v.end(),
       [](const pair<int, int> &p1, const pair<int, int> &p2) {
         return p1.first < p2.first;
       });
  int first = -1, last = -1;
  v.push_back({inf, inf});
  vector<pair<int, int>> res;
  for (int i = 0; i < v.size(); ++i) {
    if (first == -1) {
      first = v[i].first;
    } else if (v[i].first > last) {
      res.push_back({first, last});
      first = v[i].first;
    }
    last = max(last, v[i].second);
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
  int n, m;
  cin >> n >> m;
  vector<pair<int, int>> ranges[2];
  for (int i = 0; i < m; ++i) {
    int t, l, r;
    cin >> t >> l >> r;
    ranges[t].push_back({--l, --r});
  }
  ranges[1] = modify(ranges[1]);
  for (int i = 0; i < ranges[0].size(); ++i) {
    for (int j = 0; j < ranges[1].size(); ++j) {
      if (ranges[0][i].first >= ranges[1][j].first &&
          ranges[0][i].second <= ranges[1][j].second)
        return cout << "NO", 0;
    }
  }
  vector<int> res;
  res.assign(n, -1);
  int ptr = 0;
  for (int i = 0; i < n; ++i) {
    if (i == 0)
      res[i] = pow(10, 8);
    else {
      while (ptr < (int)ranges[1].size() && i > ranges[1][ptr].second) ptr++;
      if (ptr < (int)ranges[1].size()) {
        if (i == ranges[1][ptr].first) {
          res[i] = res[i - 1] - 1;
        } else if (i > ranges[1][ptr].first)
          res[i] = res[i - 1];
        else
          res[i] = res[i - 1] - 1;
      } else {
        res[i] = res[i - 1] - 1;
      }
    }
  }
  cout << "YES" << '\n';
  copy(res.begin(), res.end(), ostream_iterator<int>(cout, " "));
  return 0;
}