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;
void solve() {
  int n, m;
  cin >> n >> m;
  int t, l, r;
  vector<pair<long long, long long> > qs[2];
  for (int i = 0; i < m; i++) {
    cin >> t >> l >> r;
    l--;
    r--;
    qs[t].emplace_back(l, r);
  }
  sort(qs[1].begin(), qs[1].end());
  sort(qs[0].begin(), qs[0].end());
  vector<pair<long long, long long> > new1, new0;
  if (qs[1].size() > 0) {
    new1.push_back(qs[1][0]);
  }
  for (size_t i = 1; i < qs[1].size(); i++) {
    if (new1.back().second >= qs[1][i].first) {
      new1[new1.size() - 1].second =
          max(new1[new1.size() - 1].second, qs[1][i].second);
    } else {
      new1.push_back(qs[1][i]);
    }
  }
  if (qs[0].size() > 0) {
    new0.push_back(qs[0][0]);
  }
  for (int i = 1; i < qs[0].size(); i++) {
    if (new0.back().second >= qs[0][i].first) {
      new0[new0.size() - 1].second =
          max(new0[new0.size() - 1].second, qs[0][i].second);
    } else {
      new0.push_back(qs[0][i]);
    }
  }
  vector<int> idx(n, 0);
  int cur = 1;
  for (auto it : new0) {
    for (auto test : new1) {
      if (it.first >= test.first && it.second <= test.second) {
        cout << "NO";
        return;
      }
    }
  }
  vector<int> ans(n, -1);
  long long st = 1000001;
  for (auto it : new1) {
    for (int j = it.first; j <= it.second; j++) {
      ans[j] = st + j - it.first;
    }
    st -= 1010;
  }
  int last = 1e7;
  for (int i = 0; i < n; i++) {
    if (ans[i] != -1) {
      last = ans[i] - 1;
    } else {
      ans[i] = last--;
    }
  }
  for (auto it : qs[0]) {
    bool ok = false;
    for (int j = it.first; j < it.second; j++) {
      if (ans[j] > ans[j + 1]) {
        ok = true;
        break;
      }
    }
    if (!ok) {
      cout << "NO";
      return;
    }
  }
  cout << "YES\n";
  for (int i = 0; i < n; i++) {
    cout << ans[i] << " ";
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t = 1;
  while (t--) solve();
  return 0;
}