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;
long long ans[1005] = {0};
int main() {
  ios::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  long long i, j, n, m;
  {
    cin >> n >> m;
    vector<pair<long long, long long>> arr, brr;
    for (i = 1; i <= m; i++) {
      long long t, l, r;
      cin >> t >> l >> r;
      if (t)
        arr.push_back({l, r});
      else
        brr.push_back({l, r});
    }
    sort(arr.begin(), arr.end());
    sort(brr.begin(), brr.end());
    long long cnt = 2004;
    long long pre = -1;
    for (pair<long long, long long> k : arr) {
      if (k.first <= pre)
        for (i = pre + 1; i <= k.second; i++) ans[i] = cnt;
      else {
        cnt -= 2;
        for (i = k.first; i <= k.second; i++) ans[i] = cnt;
      }
      pre = max(pre, k.second);
    }
    cnt = 3000;
    for (pair<long long, long long> k : brr) {
      for (i = k.first; i < k.second; i++)
        if (ans[i] && ans[i + 1] && ans[i] > ans[i + 1]) break;
      if (i < k.second) continue;
      if (ans[k.first]) {
        for (i = k.first; i <= k.second; i++) {
          if (!ans[i]) {
            ans[i] = ans[k.first] - 1;
            break;
          }
        }
        if (i > k.second) {
          cout << "NO";
          return 0;
        }
      } else
        ans[k.first] = --cnt;
    }
    for (i = 1; i <= n; i++)
      if (!ans[i]) ans[i] = 1;
    cout << "YES\n";
    for (i = 1; i <= n; i++) cout << ans[i] << " ";
  }
}