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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class VasArr {

	static class FastReader { 
		BufferedReader br; 
		StringTokenizer st; 

		public FastReader() 
		{ 
			br = new BufferedReader(new
					InputStreamReader(System.in)); 
		} 

		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException  e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 

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

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

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

		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 
	}
	
	static class Node{
		int x;
		int y;
		
		Node(int x, int y){
			this.x=x;
			this.y=y;
		}
	}

	public static void main(String[] args) {

		FastReader sc = new FastReader();
		OutputStream outputstream = System.out;
		PrintWriter out = new PrintWriter(outputstream);

		int n = sc.nextInt();
		int m = sc.nextInt();
		ArrayList<Node> al = new ArrayList();
		boolean[] bools = new boolean[n+1];
		for(int i=0; i <=n; i++) bools[i] = false;
		for(int i = 0; i < m; i++){
			int t = sc.nextInt();
			int l = sc.nextInt();
			int r = sc.nextInt();
			if(t==1){
				for(int j = l+1; j <= r; j++){
					bools[j] = true;
				}
			} else {
				 al.add(new Node(l,r));
			}
		}
		int[] ans = new int[n+1];
		for(int i = 1; i <= n; i++){
			ans[i] = 1000000000;
		}
		for(Node node : al){
			//out.println(node.x + " " + node.y);
			int l = node.x;
			int r = node.y;
			boolean notFound = true;
			for(int i = l+1; i <= r; i++){
				if(bools[i]==false){
					notFound = false;
					break;
				}
			}
			if(notFound) {
				out.println("NO");
				out.close();
				return;
			}
		}
		for(int i = 2; i <= n; i++){
			if(bools[i]==false){
				int j = i;
				while(bools[j]==false){
					ans[j] = ans[j-1]-1;
					j++;
					if(j>n) break;
				}
				i=j-1;
			}
		}
		out.println("YES");
		for(int i = 1; i <= n; i++){
			out.print(ans[i] + " ");
		}
		out.println();
		out.close();
		
	}

}