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 JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.util.stream.*;

import static java.lang.Integer.parseInt;

public class m {
  private static final boolean ONLINE_JUDGE = true; //System.getProperty("ONLINE_JUDGE") != null;

  public static void main(String[] args) {
    try (BufferedReader reader = ONLINE_JUDGE ? new BufferedReader(new InputStreamReader(System.in))
                                              : new BufferedReader(new FileReader("input"));
         Writer writer = ONLINE_JUDGE ? new OutputStreamWriter(System.out) : new FileWriter("output");
         PrintWriter printWriter = new PrintWriter(writer);) {
      Solver solver = new Solver(reader, printWriter);
      while (solver.solve());
    } catch (IOException e) {
      e.printStackTrace(System.err);
    }
  }

  static final class Solver {
    final BufferedReader in;
    final PrintWriter out;

    public Solver(BufferedReader reader, PrintWriter writer) {
      in = reader;
      out = writer;
    }

    boolean solve() throws IOException {
      String line = in.readLine();
      if (line == null) {
        return false;
      }
      if (line.isEmpty()) {
        return true;
      }
      StringTokenizer tok = new StringTokenizer(line);
      int n = parseInt(tok.nextToken());
      int m = parseInt(tok.nextToken());
      int t[] = new int[m];
      int l[] = new int[m];
      int r[] = new int[m];
      for (int kk = 0; kk < m; ++kk) {
        tok = new StringTokenizer(in.readLine());
        t[kk] = parseInt(tok.nextToken());
        l[kk] = parseInt(tok.nextToken());
        r[kk] = parseInt(tok.nextToken());
      }
      int[] arr = new int[n];
      for (int i = 0; i < m; ++i) {
        if (t[i] == 1) {
          for (int j = l[i]; j < r[i]; ++j) arr[j] = 1;
        }
      }
      for (int i = 0; i < m; ++i) {
        if (t[i] == 0) {
          int newLeft = l[i];
          while (newLeft < r[i] && arr[newLeft] == 1) {
            newLeft++;
          }
          if (newLeft >= r[i]) {
            out.println("NO");
            return true;
          }
          assert arr[newLeft] == 0;
        }
      }
      int start = n + 2;
      int[] ans = new int[n + 1];
      ans[1] = start;
      for (int j = 2; j <= n; ++j) {
        if (arr[j - 1] == 0) ans[j] = ans[j - 1] - 1;
        else ans[j] = ans[j - 1] + 1;
      }
      out.println("YES");
      for (int i = 1; i <= n; ++i) {
        out.print(ans[i] + " ");
      }
      return true;
    }
  }

  static void debug(String s) {
    System.out.println(s);
  }
}