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;
inline long long add(long long a, long long b) {
  a += b;
  if (a >= 1000000007) a -= 1000000007;
  return a;
}
inline long long sub(long long a, long long b) {
  a -= b;
  if (a < 0) a += 1000000007;
  return a;
}
inline long long mul(long long a, long long b) {
  return (long long)((long long)a * b % 1000000007);
}
long long min(long long a, long long b) { return a > b ? b : a; }
long long max(long long a, long long b) { return a > b ? a : b; }
long long ar[100000];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, m;
  cin >> n >> m;
  vector<pair<long long, long long> > vc[2];
  for (int i = 0; i < m; i += 1) {
    long long t, l, r;
    cin >> t >> l >> r;
    vc[t].push_back(make_pair(l - 1, r - 1));
  }
  sort((vc[0]).begin(), (vc[0]).end());
  sort((vc[1]).begin(), (vc[1]).end());
  for (int i = 0; i < n; i += 1) {
    ar[i] = 5000 - i;
  }
  for (int i = 0; i < (int)((vc[1]).size()); i += 1) {
    for (int j = vc[1][i].first + 1; j <= vc[1][i].second; j++) {
      ar[j] = ar[j - 1];
    }
  }
  bool chk = 1;
  for (int i = 0; i < (int)((vc[0]).size()); i += 1) {
    long long cnt = 0;
    for (int j = vc[0][i].first + 1; j <= vc[0][i].second; j++) {
      if (ar[j] < ar[j - 1]) {
        cnt++;
      }
    }
    if (cnt == 0) {
      chk = 0;
      break;
    }
  }
  if (chk) {
    cout << "YES"
         << "\n";
    for (int i = 0; i < n; i += 1) cout << ar[i] << " ";
    cout << "\n";
  } else {
    cout << "NO"
         << "\n";
  }
}