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:
/* Rajkin Hossain */
import java.io.*;
import java.util.*;

public class C {
   
    FastInput k = new FastInput(System.in);
    //FastInput k = new FastInput("/home/rajkin/Desktop/input.txt");
    FastOutput z = new FastOutput();
    
    int n, m;
    
    ArrayList<Pair> sorted;
    ArrayList<Pair> unsorted;
    
    int [] mark;
    int [] ans;
    
    boolean startAlgorithm() {
    	
    	Collections.sort(sorted);
    	
    	int index = 0;
    	
    	for(int i = 0; i<sorted.size(); i++) {
    		Pair p = sorted.get(i);
    		if(mark[p.u] == 0) index++;
    		
    		while(p.u <= p.v) {
    			mark[p.u++] = index;
    		}
    	}
    	
    	for(int i = 0; i<unsorted.size(); i++) {
    		Pair p = unsorted.get(i);
    		
    		HashSet<Integer> diffIndexes = new HashSet<>();
    		int zeroCount = 0;
    		
    		while(p.u <= p.v) {
    			if(mark[p.u] == 0){
    				zeroCount++;
    			}
    			else{
    				diffIndexes.add(mark[p.u]);
    			}
    			
    			p.u++;
    		}
    		
    		if(diffIndexes.size() + zeroCount < 2) return false;
    	}
    	
    	int i = 1;
    	while(i<n) {
    		if(mark[i] == 0){
    			i++;
    		}
    		else {
    			if(mark[i] != mark[i+1]){
    				mark[i] = 0;
    			}
    			
    			i++;
    		}
    	}
    	
    	int numbering = 1;
    	for(i = 1; i<=n; i++) {
    		if(mark[i] != 0) {
    			ans[i] = numbering++;
    		}
    	}
    	
    	for(i = n; i>=1; i--) {
    		if(mark[i] == 0) {
    			ans[i] = numbering++;
    		}
    	}
    	
    	return true;
    }
    
    void startProgram() {
    	while(k.hasNext()) {
    		sorted = new ArrayList<Pair>();
    		unsorted = new ArrayList<Pair>();
    		
    		n = k.nextInt();
    		m = k.nextInt();
    		
    		mark = new int[n+1];
    		ans = new int[n+1];
    		
    		while(m-->0) {
    			int direction = k.nextInt();
    			if(direction == 0) {
    				unsorted.add(new Pair(k.nextInt(), k.nextInt()));
    			}
    			else {
    				sorted.add(new Pair(k.nextInt(), k.nextInt()));
    			}
    		}
    		
    		boolean isPossible = startAlgorithm();
    		if(isPossible) {
    			z.println("YES");
    			for(int i = 1; i<=n; i++) {
    				z.print(ans[i]+" ");
    			}
    			z.println();
    		}
    		else {
    			z.println("NO");
    		}
    	}
    	
    	z.flush();
    	System.exit(0);
    }
    
    public static void main(String [] args) throws IOException {
    	new C().startProgram();
    }
    
    class Pair implements Comparable<Pair>{
    	int u, v;
    	
		public Pair(int u, int v) {
			this.u = u;
			this.v = v;
		}
		
		@Override
		public int compareTo(Pair p) {
			return this.u - p.u;
		}
    }
    
    /* MARK: FastInput and FastOutput */
 
    class FastInput {
        BufferedReader reader;
        StringTokenizer tokenizer;
 
        FastInput(InputStream stream){
            reader = new BufferedReader(new InputStreamReader(stream));
        }
       
        FastInput(String path){
            try {
                reader = new BufferedReader(new FileReader(path));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            tokenizer = null;
        }
 
        String next() {
            return nextToken();
        }
       
        String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
           
            return null;
        }
 
        boolean hasNext(){
            try {
                return reader.ready();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return false;
        }
 
        String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = null;
                try {
                    line = reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(nextToken());
        }
       
        long nextLong() {
            return Long.valueOf(nextToken());
        }
    }
 
    class FastOutput extends PrintWriter {
          FastOutput() { super(new BufferedOutputStream(System.out)); }
    }
}