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;
const long double pi = 3.1415926536;
const long long prime = 998244353;
const long long inf = 1e18;
const long long maxN = 1e9;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n, m, t, l, r;
  cin >> n >> m;
  vector<long long> s(n + 1, 0), a(n + 1, 1000);
  vector<pair<long long, long long> > ones, zeros;
  while (m--) {
    cin >> t >> l >> r;
    if (t) {
      ones.push_back({l, r});
    } else {
      zeros.push_back({l, r});
    }
  }
  sort(ones.begin(), ones.end());
  long long last = n;
  if (!ones.empty()) {
    last = ones[0].first;
  }
  for (long long i = (long long)(2); i <= (long long)(last); i++) {
    a[i] = a[i - 1] - 1;
  }
  long long end = 1;
  for (auto &p : ones) {
    if (end < p.first) {
      for (long long i = (long long)(end + 1); i <= (long long)(p.first); i++) {
        a[i] = a[i - 1] - 1;
      }
      for (long long i = (long long)(p.first + 1); i <= (long long)(p.second);
           i++) {
        a[i] = a[i - 1];
      }
    } else {
      for (long long i = (long long)(end + 1); i <= (long long)(p.second);
           i++) {
        a[i] = a[i - 1];
      }
    }
    end = max(end, p.second);
  }
  if (!ones.empty()) {
    for (long long i = (long long)(end + 1); i <= (long long)(n); i++) {
      a[i] = a[i - 1] - 1;
    }
  }
  for (auto &p : zeros) {
    for (long long i = (long long)(p.first + 1); i <= (long long)(p.second);
         i++) {
      if (a[i] < a[i - 1]) {
        break;
      }
      if (i == p.second) {
        cout << "NO";
        return 0;
      }
    }
  }
  cout << "YES\n";
  for (long long i = (long long)(1); i <= (long long)(n); i++) {
    cout << a[i] << " ";
  }
  return 0;
}