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;
struct ST {
  long long t = 0, l = 0, r = 0;
};
bool cmp(ST st1, ST st2) { return (st1.t > st2.t); }
ST arr[10000];
long long n = 0, m = 0;
vector<pair<long long, long long> > g[10000];
bool used[10000];
long long res[10000];
void dfs(long long v) {
  used[v] = true;
  for (long long i = 0; i < g[v].size(); i++) {
    if (used[g[v][i].first] && res[v] + g[v][i].second != res[g[v][i].first]) {
      cout << "NO";
      exit(EXIT_SUCCESS);
    }
    if (!used[g[v][i].first]) {
      res[g[v][i].first] = res[v] + g[v][i].second;
      dfs(g[v][i].first);
    }
  }
}
signed main() {
  cin >> n >> m;
  for (long long i = 0; i < m; i++) {
    cin >> arr[i].t >> arr[i].l >> arr[i].r;
    arr[i].l--;
    arr[i].r--;
  }
  sort(arr, arr + m, cmp);
  for (long long i = 0; i < m; i++) {
    if (arr[i].t == 1)
      for (long long j = arr[i].l; j < arr[i].r; j++) {
        g[j].push_back({j + 1, 1});
        used[j + 1] = true;
      }
    else {
      bool flag = false;
      for (long long j = arr[i].l + 1; j <= arr[i].r; j++)
        if (!used[j]) {
          flag = true;
          g[j - 1].push_back({j, -1});
          break;
        }
      if (!flag) {
        cout << "NO";
        exit(EXIT_SUCCESS);
      }
    }
  }
  for (long long i = 0; i < n; i++) used[i] = false;
  for (long long i = 0; i < n; i++)
    if (!used[i]) {
      res[i] = (i + 1) * 1001;
      dfs(i);
    }
  cout << "YES\n";
  for (long long i = 0; i < n; i++) cout << res[i] << ' ';
  return 0;
}