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.util.*;
import java.io.*;
 
public class Solution{
	static PrintWriter out = new PrintWriter(System.out);
	public static void main (String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		
		String[] input = br.readLine().trim().split(" ");
		
    	int n = Integer.parseInt(input[0]);
    	int m = Integer.parseInt(input[1]);
    	int[] arr = new int[n];
    	for(int i = 0; i < n; i++){
    	    arr[i] = 10000 - i;
    	}
    	ArrayList<Pair> sortedIntervals = new ArrayList<>();
    	ArrayList<Pair> unsortedIntervals = new ArrayList<>();
    	while(m-- > 0){
    	    input = br.readLine().trim().split(" ");
    	    
    	    int type = Integer.parseInt(input[0]);
    	    int l = Integer.parseInt(input[1]);
    	    int r = Integer.parseInt(input[2]);
    	    
    	    if(type == 1){
    	        sortedIntervals.add(new Pair(l, r));
    	    }
    	    else{
    	        unsortedIntervals.add(new Pair(l, r));
    	    }
    	}
    	
    	Collections.sort(sortedIntervals);
    	Collections.sort(unsortedIntervals);
    	
    	ArrayList<Pair> nonOverlappingSortedIntervals = new ArrayList<>();
    	
    	for(int i = 0; i < sortedIntervals.size(); ){
    	    int j = i;
    	    int end = sortedIntervals.get(i).end;
    	    while(j < sortedIntervals.size() && end >= sortedIntervals.get(j).start){
    	        end = Math.max(end, sortedIntervals.get(j).end);
    	        j++;
    	    }
    	    nonOverlappingSortedIntervals.add(new Pair(sortedIntervals.get(i).start, end));
    	    i = j;
    	}
    	
    	
    	for(int i = 0; i < unsortedIntervals.size(); i++){
    	    for(int j = 0; j < nonOverlappingSortedIntervals.size(); j++){
    	        if(unsortedIntervals.get(i).start >= nonOverlappingSortedIntervals.get(j).start && unsortedIntervals.get(i).end <= nonOverlappingSortedIntervals.get(j).end){
    	            System.out.println("NO");
    	            return;
    	        }
    	    }
    	}
    	
    	
    	
    	for(int i = 0; i < nonOverlappingSortedIntervals.size(); i++){
    	    for(int j = nonOverlappingSortedIntervals.get(i).end - 1; j >= nonOverlappingSortedIntervals.get(i).start - 1; j--){
    	        arr[j] = arr[nonOverlappingSortedIntervals.get(i).end - 1];
    	    }
    	}
		out.println("YES");
		for(int i = 0; i < n; i++){
		    out.print(arr[i] + " ");
		}
		out.println();
		
		out.flush();
		out.close();
	}
}

class Pair implements Comparable<Pair>{
    int start;
    int end;
    
    public Pair(int start, int end)
    {
        this.start = start;
        this.end = end;
    }
    public Pair(){}
    
    public int compareTo(Pair p)
    {
        return this.start - p.start;
    }
}