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.util.*;
import javafx.util.Pair;


public class mymy
{

	static OutputStream outputStream = System.out;
	static PrintWriter out = new PrintWriter(outputStream);	
	static InputStream inputStream = System.in;
	static InputReader br = new InputReader(inputStream);

	static class node implements Comparable<node>
	{
		int l;int r;
	
		node(int i,int o)
		{
			l=i;r=o;
		}
		public int compareTo(node n)
		{
			if(this.l!=n.l) return this.l-n.l;
			return this.r-n.r;
		}
	}
	
	
	public static void main(String[] args)throws IOException
	{

		int n=br.nextInt();
		int m=br.nextInt();


		int[] a=new int[n];

		boolean flg=true;

		ArrayList<node> t1=new ArrayList<node>();
		ArrayList<node> t0=new ArrayList<node>();

		while(m-->0)
		{
			int t,l,r;
			t=br.nextInt();
			l=br.nextInt()-1;
			r=br.nextInt()-1;

			if(t==1)
			{
				t1.add(new node(l,r));
			}
			else t0.add(new node(l,r));

		}

		Collections.sort(t1);
		Collections.sort(t0);

		int curr=1000000;

		
		for(int i=0;i<t1.size();i++)
		{
			int now=curr;
			int wht=0;

			if(a[t1.get(i).l]==0)
			{
				for(int j=t1.get(i).l;j<=t1.get(i).r;j++)
				{
					a[j]=now++;
				}
			}
			else
			{
				int j=t1.get(i).l;

				while(j<=t1.get(i).r && a[j]!=0)
				{
					now=a[j];
					j++;
				}
				now++;
				while(j<=t1.get(i).r)
				{
					a[j]=now++;
					j++;
				}
			}
			curr-=1001;
		}

		int inf=999999999;

		for(int i=0;i<n;i++)
		{
			if(a[i]==0 && i==0) a[i]=inf;
			else if(a[i]==0)
			{
				a[i]=a[i-1]-1;
			}
		}


		for(int i=0;i<t0.size();i++)
		{
			boolean wht=false;

			for(int j=t0.get(i).l+1;j<=t0.get(i).r;j++)
			{
				if(a[j]<a[j-1]) wht=true;
			}

			flg&=wht;

		}

		if(flg)
		{
			out.println("YES");
			for(int i=0;i<n;i++) out.print(a[i]+" ");
				out.println();
		}
		else out.println("NO");

		

		
		



		out.close();

	}


















	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());
		}

	}
	
}