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, ans[1009], t, l, r, low = 1e8, vis[1009];
vector<pair<int, int> > v0, v1;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    cin >> t >> l >> r;
    if (t == 0)
      v0.push_back({l, r});
    else
      v1.push_back({l, r});
  }
  sort(v0.begin(), v0.end());
  sort(v1.begin(), v1.end());
  for (auto i : v1) {
    l = i.first, r = i.second;
    int b = low;
    if (ans[l] != 0)
      b = ans[l];
    else
      low -= 4000;
    while (l <= r) {
      vis[l]++;
      if (!ans[l]) ans[l] = b;
      l++;
    }
  }
  for (auto i : v0) {
    l = i.first, r = i.second;
    for (int j = l; j < r; j++) {
      if (!ans[j] && !ans[j + 1]) {
        ans[j] = 1000000000, ans[j + 1] = 1000000000 - 1;
        break;
      } else if (!ans[j]) {
        ans[j] = 1 + ans[j + 1];
        break;
      } else if (!ans[j + 1]) {
        ans[j + 1] = ans[j] - 1;
        break;
      }
    }
  }
  for (int i = 1; i <= n; i++)
    if (!ans[i]) ans[i] = 1;
  for (auto i : v0) {
    int yes = 1;
    l = i.first, r = i.second;
    for (int j = l; j < r; j++) {
      if (ans[j] > ans[j + 1]) {
        yes = 0;
        break;
      }
    }
    if (yes) return cout << "NO", 0;
  }
  cout << "YES\n";
  for (int i = 1; i <= n; i++) cout << ans[i] << " ";
  return 0;
}