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.io.*;
import java.math.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * Author: Wavator
 */
public class Main {
    public static void main(String[] args){
        InputStream inputStream = System.in;//new FileInputStream("C:\\Users\\wavator\\Downloads\\test.in");
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }

    static class Task {

        public void solve(InputReader in, PrintWriter out) {
            int n=in.nextInt(),m=in.nextInt();
            int []re=new int[n];
            for(int i=0;i<n;i++){
                re[i]=i+1;
            }
            int []me=new int[n];
            int [][] content=new int[m][3];
            for(int j=0;j<m;j++){
                if(in.nextInt()==0){
                    content[j][1]=in.nextInt();
                    content[j][2]=in.nextInt();
                }
                else{
                    content[j][0]=1;
                    int b=in.nextInt(),e=in.nextInt();
                    for(int k=b-1;k<e-1;k++){
                        me[k]=1;
                    }
                }
            }
            boolean med=true;
            for(int j=0;j<m;j++){
                if(content[j][0]==0){
                    med=false;
                    for(int k=content[j][1]-1;k<content[j][2]-1;k++){

                        if(me[k]==0){
                            med=true;

                            break;
                        }
                    }
                }
                if(!med){
                    break;
                }
            }
            if(!med){
                out.println("NO");
                out.flush();
            }
            else {
                for(int i=0;i<n;i++){
                    if(me[i]==0){
                        re[i]+=2*(n-i);
                    }
                }
                out.println("YES");
                out.flush();
                for(int i=0;i<n;i++){
                    out.print(re[i]+" ");
                    out.flush();
                }
            }
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public char[] nextCharArray() {
            return next().toCharArray();
        }

        public boolean hasNext() {
            try {
                String string = reader.readLine();
                if (string == null) {
                    return false;
                }
                tokenizer = new StringTokenizer(string);
                return tokenizer.hasMoreTokens();
            } catch(IOException e) {
                return false;
            }
        }
        public BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

        public BigDecimal nextBigDecinal() {
            return new BigDecimal(next());
        }
    }
}