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 i, j;
long long n, q, Q, t, T, m, k;
int a[1001];
int def = (int)1e8;
vector<pair<int, int> > f[2];
set<pair<int, int> > on;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n >> m;
  const int drop = n + 5;
  for (i = 0; i < m; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    b--;
    c--;
    f[a].push_back(make_pair(b, c));
  }
  for (i = 0; i < f[1].size(); i++) {
    for (j = 0; j < f[0].size(); j++) {
      if (f[1][i].first <= f[0][j].first && f[1][i].second >= f[0][j].second) {
        cout << "NO" << endl;
        exit(0);
      }
    }
  }
  for (i = 0; i < n; i++) {
    auto it = on.begin();
    while (on.size() > 0 && it != on.end()) {
      if ((*it).second < i)
        it = on.erase(it);
      else
        it++;
    }
    if (on.size() == 0) {
      def -= drop;
    }
    a[i] = def;
    def++;
    for (j = 0; j < f[1].size(); j++)
      if (f[1][j].first == i) on.insert(f[1][j]);
  }
  for (i = 0; i < f[0].size(); i++) {
    bool fl = 0;
    for (j = f[0][i].first + 1; j < f[0][i].second + 1; j++) {
      if (a[j] < a[j - 1]) fl = 1;
    }
    if (!fl) {
      cout << "NO" << endl;
      exit(0);
    }
  }
  cout << "YES" << endl;
  for (i = 0; i < n; i++) {
    if (i) cout << " ";
    cout << a[i];
  }
  cout << endl;
}