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 Main implements Runnable{
    FastScanner sc;
    PrintWriter pw;
    final class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner() {
            try {
                br = new BufferedReader(new InputStreamReader(System.in));
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                e.printStackTrace();
            }
        }
 
        public long nlo() {
            return Long.parseLong(next());
        }
 
        public String next() {
            if (st.hasMoreTokens()) return st.nextToken();
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return st.nextToken();
        }
 
        public int ni() {
            return Integer.parseInt(next());
        }
 
        public String nli() {
            String line = "";
            if (st.hasMoreTokens()) line = st.nextToken();
            else try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            while (st.hasMoreTokens()) line += " " + st.nextToken();
            return line;
        }
 
        public double nd() {
            return Double.parseDouble(next());
        }
    }
    public static void main(String[] args)
    {
        new Thread(null,new Main(),"codeforces",1<<25).start();
    }
    public void run()
    {
        sc=new FastScanner();
        pw=new PrintWriter(System.out);
        solve();
        pw.flush();
        pw.close();
    }
    public void solve()
    {
        int n=sc.ni();
        int m=sc.ni();
        int[] arr=new int[n];
        int[] krr=new int[m];
        int[] lrr=new int[m];
        int[] rrr=new int[m];
        int res=0;
        int use=10000000;
        Arrays.fill(arr,-1);
        for(int i=0;i<m;i++)
        {
            int x=sc.ni();
            int y=sc.ni()-1;int z=sc.ni()-1;
            krr[i]=x;lrr[i]=y;rrr[i]=z;
        }
        int[] tmp=new int[n];
        for(int i=0;i<n;i++)
        tmp[i]=i;
        for(int i=0;i<m;i++)
            if(krr[i]==1)
                tmp[lrr[i]]=Math.max(tmp[lrr[i]],rrr[i]);
        for(int i=0;i<n;i++)
        {
            int j=tmp[i];
            int p=i;
            while(p<=j)
                    j=Math.max(tmp[p++],j);
            if(i==j)
            continue;
            use-=10000;
            for(int k=i;k<=j;k++)
            arr[k]=use;
            i=j;
        }
        for(int i=0;i<m;i++)
        {
            if(krr[i]==0)
            {
                int l=lrr[i];
                int r=rrr[i];
                int p=0;
                for(int j=l;j<=r;j++)
                if(arr[j]==-1)
                p++;
                if(p==0)
                    if(f(arr,l,r))
                    res=-1;
                if(p==1)
                {
                    for(int j=l;j<=r;j++)
                    {
                        if(arr[j]==-1)
                        {
                            if(j==l)
                                arr[j]=arr[j+1]+1;
                            else
                            arr[j]=arr[j-1]-1;
                            break;
                        }
                    }
                }
            }
        }
        if(res==0)
        {
        pw.println("YES");
        for(int i=0;i<n;i++)
        {
            if(arr[i]!=-1)
            {
                int k=i-1;
                while((k>=0)&&(arr[k]==-1))
                {
                    arr[k]=arr[k+1]+1;
                    k--;
                }
                k=i+1;
                while(k<n&&arr[k]==-1)
                {
                    arr[k]=arr[k-1]-1;
                    k++;
                }
            }
        }
        if(arr[0]==-1)
        {
            arr[0]=10000;
            for(int i=1;i<n;i++)
            arr[i]=arr[i-1]-1;
        }
        for(int i=0;i<n;i++)
        pw.print(arr[i]+" ");
        }
        else
        pw.println("NO");
    }
    public boolean f(int[] arr,int l,int r)
    {
        for(int i=l+1;i<=r;i++)
        if(arr[i-1]>arr[i])
        return false;
        return true;
    }
}