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 n, m;
struct date {
  int t, l, r;
};
date v[1001];
int sol[1001];
bool comp(date a, date b) {
  if (a.r > b.r)
    return 1;
  else if (a.r == b.r && a.l < b.l)
    return 1;
  return 0;
}
pair<int, int> intervale[10001];
int main() {
  cin >> n >> m;
  for (int i = 1; i <= m; i++) cin >> v[i].t >> v[i].l >> v[i].r;
  sort(v + 1, v + m + 1, comp);
  int lg = 0;
  for (int i = 1; i <= m; i++)
    if (v[i].t == 1) {
      bool pus = 0;
      for (int j = 1; j <= lg; j++)
        if (!(v[i].l > intervale[j].second || v[i].r < intervale[j].first)) {
          pus = 1;
          intervale[j].first = min(intervale[j].first, v[i].l);
          intervale[j].second = max(intervale[j].second, v[i].r);
        }
      if (!pus) {
        lg++;
        intervale[lg].first = v[i].l;
        intervale[lg].second = v[i].r;
      }
    }
  for (int i = 1; i <= m; i++)
    if (v[i].t == 0) {
      for (int j = 1; j <= lg; j++)
        if (v[i].l >= intervale[j].first && v[i].r <= intervale[j].second) {
          cout << "NO";
          return 0;
        }
    }
  cout << "YES" << '\n';
  for (int i = 1; i <= n; i++) sol[i] = n - i + 1;
  for (int i = 1; i <= lg; i++) {
    int lungime = (intervale[i].second - intervale[i].first + 1);
    int adunat = intervale[i].first - 1;
    for (int j = 1; j <= lungime / 2; j++)
      swap(sol[j + adunat], sol[lungime - j + 1 + adunat]);
  }
  for (int i = 1; i <= n; i++) cout << sol[i] << " ";
  return 0;
}