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]);
            boolean b1=true;
            
            int a[]=new int[n];
            int b[]=new int[n];
            a[0]=n;
            
            int c[][]=new int[m][3];
            for(int i=0;i<m;i++)
            {
                String s2[]=br.readLine().split(" ");
                c[i][0]=Integer.parseInt(s2[0]);
                c[i][1]=Integer.parseInt(s2[1])-1;
                c[i][2]=Integer.parseInt(s2[2])-1;
            }
            
            Arrays.sort(c,new Comparator<int[]>(){
                  public int compare(final int f1[],final int f2[])
                  {
                        if(f1[0]<f2[0])
                         return 1;
                        else if(f1[0]==f2[0])
                         return 0;
                        else
                         return -1;
                  }
            });
            
            for(int i=0;i<m;i++)
            {
                  int l=c[i][1];  int r=c[i][2];
               if(c[i][0]==1)
               {
                     for(int j=l+1;j<=r;j++)
                      b[j]=1;
               }
               else
               {
                     boolean bb=false;
                     for(int j=l+1;j<=r;j++)
                      if(b[j]<=0)
                      { b[j]=-1; bb=true; }
                     if(!bb)
                      b1=false;
               }
            }
            
            for(int i=1;i<n;i++)
             a[i]=a[i-1]+b[i];
            
            StringBuffer sb=new StringBuffer("YES");
            sb.append("\n");
            for(int i=0;i<n;i++)
             sb.append(a[i]).append(" ");
            if(!b1)
             sb=new StringBuffer("NO");
            
            System.out.println(sb);
      }
}