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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.StringTokenizer;

public class cf {
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
		//it reads the data about the specified point and divide the data about it ,it is quite fast
		//than using direct 

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

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}
	static int sum(int n)
	{int s=0;
		while(n!=0)
		{
			s+=n%10;
			n/=10;
		}
		return s;
	}
	
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	static class Pair{
        int x;int y;
        Pair(int x,int y){
            this.x=x;
            this.y=y;
          //  this.i=i;
        }
    }
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		HashMap<Integer,Integer>map=new HashMap<Integer,Integer>();
		FastReader in=new FastReader();
	int n=in.nextInt();
	int m=in.nextInt();
	int a[]=new int[n];int p[]=new int[n];int k=0;
	int u=0;
	Pair ar[]=new Pair[n];int o=n;
	while(m-->0)
	{
		int t=in.nextInt();
		int l=in.nextInt()-1;
		int r=in.nextInt()-1;
	if(t==1)
	{
		for(int i=l;i<r;i++)
			a[i]=1;
	}
	else
	{
	ar[k++]=new Pair(l,r);
	}

	}
	for(int i=0;i<o;i++)
	{
		if(a[i]==1)
			a[i]=n;
		else
			a[i]=n--;
	}
	int flag=1;
	for(int i=0;i<k;i++){
        int check=0;
        int l=ar[i].x;int r=ar[i].y;
        int el=a[l];
        for(int j=l+1;j<=r;j++){
            if(el!=a[j]){
                check=1;
            }
        }
        if(check==0){
            flag=0;
            break;
        }
    }
    if(flag==0){
        System.out.println("NO");
    }
    else{
        System.out.println("YES");
        for(int i=0;i<o;i++){
            System.out.print(a[i]+" ");
        }
    }
	
	}

}