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(0), cin.tie(0);
  int n, m;
  cin >> n >> m;
  vector<pair<int, int>> s, ns;
  for (int t, l, r, i = 0; i < m; ++i) {
    cin >> t >> l >> r;
    --l, --r;
    if (t == 1)
      s.push_back({l, r});
    else
      ns.push_back({l, r});
  }
  auto cs = s;
  vector<int> a(n);
  for (int i = 0; i < s.size(); ++i)
    for (int j = i + 1; j < s.size(); ++j) {
      if (s[j].first <= s[i].second && s[j].second >= s[i].first) {
        s[i].first = min(s[i].first, s[j].first);
        s[i].second = max(s[i].second, s[j].second);
        s.erase(s.begin() + j);
        --i;
        break;
      }
      swap(s[i], s[j]);
      if (s[j].first <= s[i].second && s[j].second >= s[i].first) {
        s[i].first = min(s[i].first, s[j].first);
        s[i].second = max(s[i].second, s[j].second);
        s.erase(s.begin() + j);
        --i;
        break;
      }
      swap(s[i], s[j]);
    }
  sort(s.begin(), s.end());
  int k = n + 1, p = 0;
  for (int i = 0; i < n; ++i, --k) {
    if (p < s.size() && s[p].first == i) {
      for (; i <= s[p].second; ++i) a[i] = k;
      --i;
      ++p;
      continue;
    }
    a[i] = k;
  }
  auto sorted = [&](int l, int r) {
    bool ok = true;
    int last = -1;
    for (; l <= r; ++l) {
      ok &= a[l] >= last;
      last = a[l];
    }
    return ok;
  };
  bool ok = true;
  for (auto i : cs) ok &= sorted(i.first, i.second);
  for (auto i : ns) ok &= !sorted(i.first, i.second);
  if (ok) {
    cout << "YES\n";
    for (auto &i : a) cout << i << " \n"[&i == &a.back()];
  } else
    cout << "NO\n";
  return 0;
}