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.util.ArrayDeque;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.List;
import java.util.Queue;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    int n = in.nextInt();
    int m = in.nextInt();

    Fact[] facts = new Fact[m];
    for (int i = 0; i < m; i += 1) {
      facts[i] = new Fact(in.nextInt(), in.nextInt() - 1, in.nextInt() - 1);
    }
    Arrays.sort(facts);

    Graph graph = new Graph(n);
    boolean valid = true;

    for (Fact f : facts) {
      if (f.type == 1) {
        graph.addNormal(f.left, f.right);
      } else {
        valid = (valid && graph.addReverse(f.left, f.right));
      }
    }

    List<Integer> sorted = graph.topoSort();
    if (!valid || sorted == null) {
      System.out.println("NO");
      return;
    }

    int[] res = new int[n];
    for (int i = 0; i < n; i += 1) {
      res[sorted.get(i)] = i + 1;
    }

    System.out.println("YES");
    for (int i = 0; i < n; i += 1) {
      System.out.print(res[i] + " ");
    }
    System.out.println();
  }
}

class Fact implements Comparable<Fact> {
  public int type;
  public int left;
  public int right;

  public Fact(int type, int left, int right) {
    this.type = type;
    this.left = left;
    this.right = right;
  }

  @Override
  public int compareTo(Fact other) {
    if (type != other.type) {
      return other.type - type;
    }
    if (left != other.left) {
      return left - other.left;
    }
    return right - other.right;
  }
}

class Graph {
  private Node[] nodes;

  public Graph(int size) {
    nodes = new Node[size];
    for (int i = 0; i < size; i += 1) {
      nodes[i] = new Node();
    }
  }

  public void addNormal(int left, int right) {
    for (int i = left; i + 1 <= right; i += 1) {
      addEdge(i, i + 1);
    }
  }

  public boolean addReverse(int left, int right) {
    for (int i = left; i + 1 <= right; i += 1) {
      if (!nodes[i].hasEdge(i + 1)) {
        addEdge(i + 1, i);
        return true;
      }
    }
    return false;
  }

  private void addEdge(int source, int dest) {
    nodes[source].edges.add(dest);
    nodes[dest].degree += 1;
  }

  public List<Integer> topoSort() {
    Queue<Integer> queue = new ArrayDeque<Integer>();
    for (int i = 0; i < nodes.length; i += 1) {
      if (nodes[i].degree == 0) {
        queue.add(i);
      }
    }

    List<Integer> sorted = new ArrayList<Integer>();
    while (queue.size() > 0) {
      int node = queue.poll();
      sorted.add(node);

      for (int next : nodes[node].edges) {
        nodes[next].degree -= 1;
        if (nodes[next].degree == 0) {
          queue.add(next);
        }
      }
    }

    if (sorted.size() != nodes.length) {
      return null;
    }
    return sorted;
  }
}

class Node {
  public List<Integer> edges;
  public int degree;

  public Node() {
    edges = new ArrayList<Integer>();
    degree = 0;
  }

  public boolean hasEdge(int dest) {
    return edges.contains(dest);
  }
}