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.*;
import java.lang.*;
import java.io.*;
 
 public class Solution{
 static int l1=-1;
    static int l0=-1;
    public static boolean findArray(int[] a, int[] q){
            
          if(q[0] == 1){
              if(q[1] <= l0){
                  int val = a[q[1]];
                 for(int i=q[1]+1; i<=q[2]; i++)
                 a[i] = val;
               }
              l1 = Math.max(q[2],l1);
          }
          else{
              if(q[2] <= l1)
               return false;
               
               int val = a[q[1]] - 1;
              for(int i = q[1]+1; i<=q[2]; i++){
               if(i <= l1)
                continue;
               a[i] = val;
              }
              
              l0 = Math.max(l0,q[2]);
          }

        return true;
    }
    
	public static void main (String[] args) throws java.lang.Exception
	{
	   InputStreamReader in = new InputStreamReader(System.in);
	   BufferedReader br = new BufferedReader(in); 
	    OutputStream output = System.out;
       PrintWriter out = new PrintWriter(output);
	   StringTokenizer st = new StringTokenizer(br.readLine());
	   
	   int n = Integer.parseInt(st.nextToken());
	   int[] a = new int[n];
	   List<int[]> zero = new ArrayList();
	   List<int[]> ones = new ArrayList();
	   
        int task = Integer.parseInt(st.nextToken());
        Arrays.fill(a,1000);
        
        Comparator<int[]> comp= new Comparator<int[]>(){
 
             public int compare(int[] a, int[] b){
                 if(a[1] == b[1])
                  return a[2]-b[2];
                  
                  return a[1]-b[1];
             }
         };
        PriorityQueue<int[]> pq = new PriorityQueue(n,comp);      
  
       for(int i=0; i<task; i++){
          st = new StringTokenizer(br.readLine());
           int t = Integer.parseInt(st.nextToken());
           int l = Integer.parseInt(st.nextToken())-1;
           int r = Integer.parseInt(st.nextToken())-1;
           
            pq.offer(new int[]{t,l,r});
            if(t == 0)
             zero.add(new int[]{l,r});
             else
             ones.add(new int[]{l,r});
       }
           while(pq.size()>0){
              int[] t = pq.poll();
              
              if(!findArray(a,t)){
               out.println("NO");
               out.close();
               return;
            }
        }
         
         for(int[]z : zero){
             int l = z[0];
             int r = z[1];
             
             boolean flag = true;
             
             for(int i=l; i<r; i++)
                 if(a[i]>a[i+1]){
                     flag = false;
                     break;
                 }
             if(flag){
               out.println("NO");
               out.close();
               return;
             }
         }
                    
         out.println("YES");
        for(int i=0; i<a.length; i++)
          out.print(a[i]+" ");
          
        out.close();
	}  
	}