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(false);
  cin.tie(0);
  cout.tie(0);
  int n, m;
  cin >> n >> m;
  vector<int> col(n, 10000);
  vector<pair<int, int>> col1, col2, col3;
  for (int i = 0; i != m; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    b--;
    c--;
    if (a) {
      col1.push_back({b, c});
    } else {
      col2.push_back({b, c});
    }
  }
  sort(col2.begin(), col2.end());
  sort(col1.begin(), col1.end());
  for (int i = 1; i < col1.size(); i++) {
    if (col1[i].first <= col1[i - 1].second) {
      col1[i].first = min(col1[i].first, col1[i - 1].first);
      col1[i].second = max(col1[i].second, col1[i - 1].second);
    } else {
      col3.push_back(col1[i - 1]);
    }
  }
  if (col1.size() > 0) {
    col3.push_back(col1[col1.size() - 1]);
  }
  for (int i = 0; i < col2.size(); i++) {
    for (int j = 0; j < col3.size(); j++) {
      if (col2[i].first >= col3[j].first && col2[i].second <= col3[j].second) {
        cout << "NO";
        return 0;
      }
    }
  }
  vector<int> ans;
  if (col3.size() > 0) {
    for (int j = 0; j < col3[0].first; j++) {
      ans.push_back(j);
    }
    for (int i = 0; i < col3.size() - 1; i++) {
      ans.push_back(col3[i].first);
      for (int j = col3[i].second + 1; j < col3[i + 1].first; j++) {
        ans.push_back(j);
      }
    }
    ans.push_back(col3[col3.size() - 1].first);
    for (int j = col3[col3.size() - 1].second + 1; j < n; j++) {
      ans.push_back(j);
    }
  } else {
    for (int i = 0; i != n; i++) {
      ans.push_back(i);
    }
  }
  int cur = 10000;
  for (int i = 0; i != ans.size(); i++) {
    cur--;
    col[ans[i]] = cur;
  }
  cout << "YES\n";
  for (int i = 0; i != n; i++) {
    cout << col[i] << " ";
  }
  return 0;
}