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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

import com.sun.media.sound.AlawCodec;
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)),true);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.flush();
		out.close();
	}
}

class TaskB {
    public void solve(int testNumber, InputReader in, PrintWriter pw) {
    	int n=in.nextInt();
    	int m=in.nextInt();
    	int ans[]=new int[n+1];
    	int b[]=new int[n];
    	Arrays.fill(b, -1);
    	ArrayList<Range> al=new ArrayList<Range>();
    	for(int i=0;i<m;i++) {
    		int t=in.nextInt();
    		int l=in.nextInt();
    		int r=in.nextInt();
    		Range range=new Range(t,l,r);
    		if(t==1) {
    			for(int j=l;j<r;j++) {
    				b[j]=0;
    			}
    		}else {
    			al.add(range);
    		}
    	}
    	ans[1]=n;
    	for(int i=1;i<n;i++) {
    		ans[i+1]=b[i]+ans[i];
    	}
    	boolean flag=true;
    	for(Range range:al) {
    		if(isSorted(range,ans)) {
    			pw.println("NO");
    			return;
    		}
    	}
        pw.println("YES");
        for (int i = 1; i <= n; i++) {
            pw.print(ans[i] + " ");
        }
    	
    	
}
    public boolean isSorted(Range range,int arr[]) {
    	int l=range.l;
    	int r=range.r;
    	for (int i = l; i < r; i++) {
            if (arr[i] > arr[i + 1]) {
                return false;
            }
        }
        return true;
    }
}
class Range{
	int t;
	int l;
	int r;
	Range(int t,int l,int r){
		this.t=t;
		this.l=l;
		this.r=r;
	}
}
class Pair<A,B>{	
	A first;
	B second;
	Pair(A first,B second){
		this.first=first;
		this.second=second;
	}
}


class InputReader{
    BufferedReader br;
    StringTokenizer st;
    public InputReader(InputStream in){
        br=new BufferedReader(new InputStreamReader(in));
        st=null;
    }
    public String next(){
    while(st==null||!st.hasMoreTokens()){
        try{
            st=new StringTokenizer(br.readLine());
        }catch(IOException e){
            throw new RuntimeException(e);
        }
    }
   return st.nextToken();
    }
    public int nextInt(){
        return Integer.parseInt(next());
    }
    public long nextLong() {
    	return Long.parseLong(next());
    }
    public double nextDouble() {
    	return Double.parseDouble(next());
    }
}