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;
bool cmp(pair<int, int> &a, pair<int, int> &b) {
  if (a.second < b.second) return true;
  return false;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, m, flag = 1, t, l, r, flag_, s = 0;
  cin >> n >> m;
  int c = 0;
  vector<int> ans(n + 1, -1), a(n + 1, 0);
  vector<pair<int, int>> p;
  for (int j = 0; j < m; j++) {
    cin >> t >> l >> r;
    if (t == 0) {
      p.push_back(make_pair(l, r));
      s++;
      continue;
    }
    for (int i = l + 1; i <= r; i++) ans[i] = 1;
  }
  sort(p.begin(), p.end(), cmp);
  for (int j = 0; j < s; j++) {
    l = p[j].first;
    r = p[j].second;
    flag_ = 0;
    for (int i = l + 1; i <= r; i++) {
      if (ans[i] == 0) {
        flag_ = 1;
        break;
      }
    }
    if (flag_ == 0) {
      for (int i = l + 1; i <= r; i++) {
        if (ans[i] == -1) {
          ans[i] = 0;
          flag_ = 1;
          break;
        }
      }
    }
    if (flag_ == 0) {
      flag = 0;
      break;
    }
  }
  if (flag == 0) {
    cout << "NO" << endl;
    return 0;
  }
  cout << "YES" << endl;
  int i = 1, j, mid;
  while (i < n) {
    if (ans[i + 1] == 0) {
      a[i] = 1000000000;
      i++;
      while (i <= n && ans[i] == 0) {
        a[i] = a[i - 1] - 1;
        i++;
      }
    } else
      i++;
  }
  if (a[1] == 0) a[1] = 1;
  for (int i = 2; i <= n; i++) {
    if ((ans[i] == 1 || ans[i] == -1) && a[i] == 0) a[i] = a[i - 1];
  }
  for (int i = 1; i <= n; i++) cout << a[i] << " ";
  return 0;
}