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;
long long id[10005];
long long root(long long x) {
  while (id[x] != x) {
    id[x] = id[id[x]];
    x = id[x];
  }
  return x;
}
void unio(long long x, long long y) { id[root(y)] = root(x); }
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  long long n, m;
  cin >> n >> m;
  for (long long i = 0; i < n + 5; i++) {
    id[i] = i;
  }
  vector<pair<long long, pair<long long, long long>>> v;
  for (long long i = 0; i < m; i++) {
    long long t, x, y;
    cin >> t >> x >> y;
    v.push_back(make_pair(1 - t, make_pair(x, y)));
  }
  sort(v.begin(), v.end());
  long long arr[n + 1];
  for (long long i = 0; i < n; i++) {
    arr[i + 1] = 1;
  }
  long long flag = 0, val = 10000;
  for (long long i = 0; i < m; i++) {
    if (v[i].first == 0) {
      long long temp = v[i].second.first;
      for (long long j = v[i].second.first; j < v[i].second.second + 1; j++) {
        unio(temp, j);
      }
    } else {
      long long x = v[i].second.first, y = v[i].second.second;
      if (root(x) != root(y)) {
        if (arr[root(x)] == 1) {
          arr[root(x)] = val;
        }
        arr[root(y)] = arr[root(x)] - 1;
        val -= 2;
      } else {
        flag = 1;
        break;
      }
    }
  }
  if (flag == 1) {
    cout << "NO" << endl;
  } else {
    cout << "YES" << endl;
    for (long long i = 0; i < n; i++) {
      arr[i + 1] = arr[root(i + 1)];
      cout << arr[i + 1] << " ";
    }
  }
}