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(NULL);
  int n, m, i, l, r, t, j, seg;
  cin >> n >> m;
  vector<pair<int, int>> un;
  vector<pair<int, int>> so;
  for (i = 0; i < m; i++) {
    cin >> t >> l >> r;
    if (t == 1) {
      so.push_back({l, r});
    } else {
      un.push_back({l, r});
    }
  }
  if (so.size() == 0) {
    cout << "YES" << endl;
    for (int i = 0; i <= n - 1; i++) {
      cout << n - i << " ";
    }
  } else {
    sort(so.begin(), so.end());
    int segment[1001] = {0};
    seg = 1;
    for (i = so[0].first; i <= so[0].second; i++) {
      segment[i] = 1;
    }
    int maxr = so[0].second;
    for (i = 1; i < so.size(); i++) {
      seg += (so[i].first > maxr);
      maxr = max(maxr, so[i].second);
      for (j = so[i].first; j <= so[i].second; j++) {
        segment[j] = seg;
      }
    }
    int bc = -1;
    for (j = 0; j < un.size(); j++) {
      bc = -1;
      int same = segment[un[j].first];
      for (i = un[j].first + 1; i <= un[j].second; i++) {
        if (segment[i] == 0 || segment[i] != same) {
          bc = 0;
          break;
        }
      }
      if (bc == -1) {
        break;
      }
    }
    if (bc == -1 && un.size() != 0) {
      cout << "NO" << endl;
    } else {
      cout << "YES" << endl;
      int ny = 1000;
      cout << ny << " ";
      int curr = segment[1];
      for (i = 2; i <= n; i++) {
        ny -= (segment[i] != curr || (segment[i] == 0));
        cout << ny << " ";
        curr = segment[i];
      }
    }
  }
  return 0;
}