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() {
  int n, m;
  cin >> n >> m;
  vector<pair<int, int>> ia, da;
  for (int i = 0; i < m; ++i) {
    int t, a, b;
    cin >> t >> a >> b;
    if (t)
      ia.push_back(make_pair(a, b));
    else
      da.push_back(make_pair(a, b));
  }
  sort(ia.begin(), ia.end());
  vector<pair<int, int>> aa;
  int a = 0, b = 0;
  for (int i = 0; i < ia.size(); ++i) {
    int ta = ia[i].first, tb = ia[i].second;
    if (a == 0) {
      a = ta, b = tb;
    } else if (ta > b) {
      aa.push_back(make_pair(a, b));
      a = ta, b = tb;
    } else {
      b = ((b > tb) ? (b) : (tb));
    }
  }
  if (a != 0) aa.push_back(make_pair(a, b));
  vector<int> an(n, 0);
  for (int i = 0; i < aa.size(); ++i) {
    int a = aa[i].first, b = aa[i].second;
    int t = 1000000 - i * 1000;
    for (int j = a; j < b + 1; ++j) an[j - 1] = t;
  }
  int t = 1;
  for (int i = n - 1; i >= 0; --i) {
    if (an[i] == 0) an[i] = t;
    t = ((t > an[i]) ? (t) : (an[i])) + 1;
  }
  for (int i = 0; i < da.size(); ++i) {
    int ok = 0;
    int a = da[i].first, b = da[i].second;
    for (int j = a; j < b; ++j)
      if (an[j - 1] > an[j]) {
        ok = 1;
        break;
      }
    if (!ok) {
      cout << "NO" << endl;
      return 0;
    }
  }
  cout << "YES" << endl;
  for (int i = 0; i < n; ++i) cout << an[i] << " ";
  cout << endl;
}