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;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n, m;
  cin >> n >> m;
  vector<long long> v(n + 1, 0);
  vector<pair<long long, long long>> inc, dec;
  for (long long i = 0; i < m; i++) {
    long long t, l, r;
    cin >> t >> l >> r;
    if (t)
      inc.push_back({l, r});
    else
      dec.push_back({l, r});
  }
  sort(inc.begin(), inc.end());
  long long start = 2000001;
  for (auto it : inc) {
    for (long long i = it.first; i <= it.second; i++) {
      if (v[i])
        ;
      else {
        if (i == it.first) {
          v[i] = start;
        } else
          v[i] = v[i - 1] + 1;
      }
    }
    start -= 1000;
  }
  for (long long i = 1; i <= n; i++) {
    if (v[i] == 0) {
      if (i == 1)
        v[i] = 30000000;
      else
        v[i] = v[i - 1] - 1;
    }
  }
  cerr << v[1];
  bool ch = 1;
  for (auto it : dec) {
    if (it.second - it.first == 0) {
      ch = 0;
      break;
    }
    bool ok = 0;
    for (long long i = it.first + 1; i <= it.second; i++) {
      if (v[i] < v[i - 1]) ok = 1;
    }
    ch &= ok;
  }
  if (ch) {
    cout << "YES"
         << "\n";
    for (long long i = 1; i <= n; i++) cout << v[i] << " ";
  } else
    cout << "NO";
}