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 main() {
  int n, m, i, j;
  cin >> n >> m;
  int a[n], mark[n], s = 1, t[m], l[m], r[m];
  for (i = 0; i < n; i++) mark[i] = 0;
  for (i = 0; i < m; i++) {
    cin >> t[i] >> l[i] >> r[i];
    int b = mark[r[i] - 1], a = mark[l[i] - 1];
    if (a > 0 && t[i] > 0) {
      for (j = l[i] - 1; j < r[i]; j++) {
        mark[j] = a;
      }
      if (b > 0) {
        int p = r[i];
        while (p < n && mark[p] == b) {
          mark[p++] = mark[r[i] - 1];
        }
      }
    } else if (b > 0 && t[i] > 0) {
      for (j = l[i] - 1; j < r[i]; j++) {
        mark[j] = b;
      }
      if (a > 0) {
        int p = l[i] - 2;
        while (p >= 0 && mark[p] == a) {
          mark[p--] = mark[l[i] - 1];
        }
      }
    } else if (t[i] > 0) {
      for (j = l[i] - 1; j < r[i]; j++) {
        mark[j] = s;
      }
      s++;
    }
  }
  int flag = 0;
  for (i = 0; i < m; i++) {
    if (t[i] == 0) {
      int p = mark[l[i] - 1], u = 0;
      for (j = l[i] - 1; j < r[i]; j++) {
        if (mark[j] != p) u = 1;
      }
      if (u == 0 && mark[l[i] - 1]) {
        flag = 1;
        break;
      }
    }
  }
  if (flag == 1)
    cout << "NO" << endl;
  else {
    a[0] = n + 1;
    for (i = 1; i < n; i++) {
      if (mark[i] > 0 && mark[i - 1] == mark[i])
        a[i] = a[i - 1] + 1;
      else {
        a[i] = a[i - 1] - 1;
      }
    }
    cout << "YES" << endl;
    for (i = 0; i < n; i++) cout << a[i] << " ";
  }
  return 0;
}