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.io.*;
public class A
{
      public static void main(String ar[]) throws Exception
      {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String s1[]=br.readLine().split(" ");
            int n=Integer.parseInt(s1[0]);
            int m=Integer.parseInt(s1[1]);
            
            StringBuffer sb=new StringBuffer();
            int b[]=new int[n+1];
            int c[]=new int[n+1];
            ArrayList<ArrayList<Integer>> al=new ArrayList();
            for(int i=0;i<m;i++)
            {
                String s2[]=br.readLine().split(" ");
                ArrayList<Integer> al1=new ArrayList<Integer>();
                int t=Integer.parseInt(s2[0]);
                int l=Integer.parseInt(s2[1]);
                int r=Integer.parseInt(s2[2]);
                if(t==0)
                { c[l]+=-1;  c[r]+=1; al1.add(l); al1.add(r); al.add(al1); }
                else
                { b[l]+=1; b[r]+=-1; }
            }
            
            for(int i=1;i<n;i++)
            { b[i]+=b[i-1]; c[i]+=c[i-1]; }
            
            int a[]=new int[n];
             a[0]=1;  int x=1;
            if(c[0]<0 && b[0]<=0)
            { a[0]=5000;  x=1000; }
            
            
            for(int i=1;i<n;i++)
            {
                  if(b[i]>0 || (b[i]==0 && c[i]==0))
                  { a[i]=x+1; x++; }
                  else
                  { a[i]=x-1; x--; }
            }
            int min=Integer.MAX_VALUE;
            min=a[0];
            TreeSet<Integer> ts=new TreeSet<Integer>();
            for(int i=1;i<n;i++)
            {
            if(a[i]<a[i-1])
              ts.add(i);
            min=Math.min(min,a[i]);
            }
            
            min--;
            for(int i=0;i<n;i++)
            { a[i]-=min; sb.append(a[i]).append(" "); }
            boolean bb=true;
            for(int i=0;i<al.size();i++)
            {
                  int u=al.get(i).get(0);
                  int v=al.get(i).get(1);
                  if((ts.subSet(u,v+1)).size()==0)
                   bb=false;
            }
            if(bb)
            {
            System.out.println("YES");
            System.out.println(sb);
            }
            else
             System.out.println("NO");
      }
}