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() {
  long long n, m, i, t, a, b, j1 = 0, j2 = 0, j, x;
  cin >> n >> m;
  bool isans = true;
  long long ans[n + 1];
  for (i = 0; i <= n; i++) ans[i] = n - i + 1;
  pair<long long, long long> p;
  pair<long long, long long> arr[n], brr[n];
  for (i = 0; i < m; i++) {
    cin >> t >> a >> b;
    if (t)
      arr[j1++] = {a, b};
    else
      brr[j2++] = {a, b};
  }
  sort(arr, arr + j1);
  sort(brr, brr + j2);
  for (i = 0; i < j1; i++) {
    p = arr[i];
    for (j = p.first; j <= p.second; j++) ans[j] = ans[p.first];
  }
  for (i = 0; i < j2; i++) {
    p = brr[i];
    x = 0;
    for (j = p.first; j < p.second; j++)
      if (ans[j] > ans[j + 1]) x = 1;
    if (!x) isans = false;
  }
  if (isans) {
    cout << "YES" << endl;
    for (i = 1; i <= n; i++) cout << ans[i] << " ";
    cout << endl;
  } else
    cout << "NO" << endl;
  return 0;
}