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.*;

public class C {

	void run() {
		int n = in.nextInt();
		int m = in.nextInt();

		ArrayList<Interval> q1 = new ArrayList<>();
		ArrayList<Interval> q0 = new ArrayList<>();
		int i,j,l,r,tt;

		for(i=0;i<m;i++){
			tt = in.nextInt();
			l = in.nextInt();
			r = in.nextInt();
			if(tt == 1)
				q1.add(new Interval(l,r));
			else
				q0.add(new Interval(l,r));
		}
		//sort and merge q1
		q1.sort(Comparator.comparingInt(ii -> ii.l));
		ArrayList<Interval> q1_ = new ArrayList<>();

		l = -1; r = -1;
		for(Interval w : q1){
			if(l == -1){ // open
				l = w.l;
				r = w.r;
				continue;
			}
			if(w.l > r){
				// close prev + open new
				q1_.add(new Interval(l,r));
				l = w.l; r = w.r;
			}else{
				// merge
				r = Math.max(r, w.r);
			}
		}
		if(l != -1)
			q1_.add(new Interval(l,r));

		q1 = q1_;

		// I in q0 inside I´ in q1 ? NO : YES
		q0.sort(Comparator.comparingInt(ii -> ii.l));
		i = 0;
		boolean fail = false;
		for(Interval w : q0){
			if(i >= q1.size()) break;
			Interval ref = q1.get(i);
			while(ref.r < w.l){
				i++;
				if(i >= q1.size()) break;
				ref = q1.get(i);
			}
			if(ref.r < w.l) break;
			//ref.r >= w.l
			if(w.l >= ref.l && w.r <= ref.r){
				fail = true;
				break;
			}
		}
		if(fail){
			out.println("NO");
			return;
		}
		
		// build ans
		int ans[] = new int[n+1];
		int minV = Integer.MAX_VALUE;
		j = 0;
		for(i = 1; i<= n; i++){
			int inc = -1;
			if(j < q1.size()){
				Interval ref = q1.get(j);
				if(i > ref.l && i <= ref.r){
					inc = 1;
				}
				if(i == ref.r) j++;
			}
			ans[i] = ans[i-1] + inc;
			minV = Math.min(minV, ans[i]);
		}

		out.println("YES");
		for(i=1;i<=n;i++)
			out.print((-minV + ans[i] + 1) + " ");
		out.println();


	}

	class Interval{
		int l,r;
		Interval(int l_, int r_) {l = l_; r = r_;}
	}
	
	static MyScanner in;
	static PrintWriter out;

	public static void main(String[] args) throws IOException {
		boolean stdStream = true;
		if(stdStream){
			in = new MyScanner();
			out = new PrintWriter(System.out);
		}else{
			String fileName = C.class.getSimpleName();
			int n_test = 1;			
			String inputFileName = fileName + String.format(".%02d", n_test) + ".inp";
			String outputFileName = fileName + String.format(".%02d", n_test) + ".out";
			in = new MyScanner(new BufferedReader(new FileReader(inputFileName)));
			out = new PrintWriter(outputFileName);
		}
			
		new C().run();

		in.close();
		out.close();
	}

	static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

        MyScanner(){
            this.br = new BufferedReader(new InputStreamReader(System.in));
        }

		MyScanner(BufferedReader br) {
			this.br = br;
        }

        void close() throws IOException {
            br.close();
        }
        
		void findToken() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
		}
		
		String next() {
			findToken();
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}