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, i, j, x, y, z;
  int arr[10005] = {0};
  vector<pair<int, int> > v[4];
  cin >> n >> m;
  for (i = 0; i < m; i++) {
    cin >> x >> y >> z;
    v[x].push_back({y, z});
  }
  if (v[1].size() == 0) {
    int a = n + 1;
    cout << "YES\n";
    for (i = 1; i <= n; i++) cout << a-- << " ";
    return 0;
  }
  sort(v[1].begin(), v[1].end());
  stack<pair<int, int> > st;
  st.push(v[1][0]);
  for (i = 1; i < v[1].size(); i++) {
    int x = st.top().first;
    int y = st.top().second;
    if (y >= v[1][i].first) {
      y = max(y, v[1][i].second);
      st.pop();
      st.push({x, y});
    } else {
      st.push(v[1][i]);
    }
  }
  while (!st.empty()) {
    v[2].push_back(st.top());
    st.pop();
  }
  reverse(v[2].begin(), v[2].end());
  int a = n + 1;
  for (i = 0; i < v[2].size(); i++) {
    for (j = v[2][i].first; j <= v[2][i].second; j++) arr[j] = a * n;
    --a;
  }
  if (arr[1] == 0) arr[1] = (n + 2) * n;
  for (i = 1; i <= n; i++)
    if (arr[i] == 0) arr[i] = arr[i - 1] - 1;
  for (i = 0; i < v[0].size(); i++) {
    bool flag = false;
    for (j = v[0][i].first; j < v[0][i].second; j++)
      if (arr[j + 1] < arr[j]) {
        flag = true;
        break;
      }
    if (flag == false) {
      cout << "NO";
      return 0;
    }
  }
  cout << "YES\n";
  for (i = 1; i <= n; i++) cout << arr[i] << " ";
}