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.StringTokenizer;
import java.util.Arrays; 
import java.util.HashSet; 
import java.util.Comparator;
import java.util.List; 
import java.util.ArrayList;



public class VasyaAndArray {


    public static void main(String[] args) throws IOException {
	
	    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
        StringTokenizer tokenizer;


	    tokenizer = new StringTokenizer(reader.readLine());
        int n = Integer.parseInt(tokenizer.nextToken());
        int m = Integer.parseInt(tokenizer.nextToken());

        int[][] ranges = new int[m][3];
        int numIncreasingRanges = 0; 
        for(int i = 0; i < m; i++){
            tokenizer = new StringTokenizer(reader.readLine());
            ranges[i][0] = Integer.parseInt(tokenizer.nextToken());
            ranges[i][1] = Integer.parseInt(tokenizer.nextToken());
            ranges[i][2] = Integer.parseInt(tokenizer.nextToken());
            if(ranges[i][0] == 1){
                numIncreasingRanges++;
            }
        }

        Arrays.sort(ranges, new Comparator<int[]>(){
            @Override
            public int compare(int[] a, int[] b){
                if(a[0] > b[0]){
                    return - 1;
                } else if(a[0] == b[0]){
                    if(a[1] < b[1]){
                        return -1;
                    } else if(a[1] == b[1]){
                        return 0; 
                    } else {
                        return 1; 
                    }
                    
                } else {
                    return 1; 
                }
            }
        });

        List<int[]> increasingRanges = new ArrayList<>();
        int s = 0; 
        int e = 0;
        
        for(int i = 0; i<numIncreasingRanges; i++) {
        
            int[] range = ranges[i];
 
            if(range[1] > e){
                if(i != 0){
                    increasingRanges.add(new int[]{s, e});
                }
                s = range[1];
                e = range[2];
            }

            if(range[2] > e){
                e = range[2];
            }
        }
        increasingRanges.add(new int[]{s, e});

        //checking for if any t = 0 range has both start and end in the set. 
        for(int i = numIncreasingRanges; i<m; i++){
            int[] range = ranges[i];
            for(int j = 0; j<increasingRanges.size(); j++){
                if(increasingRanges.get(j)[0] <= range[1] && increasingRanges.get(j)[1] >= range[2]){
                    writer.write("NO");
                    writer.flush(); 
                    return; 
                } 
            }
        }
        writer.write("YES");
        writer.newLine();
        writer.flush(); 
        int start = 10001; 

        int index = 1; 
        for(int i = 0; i<increasingRanges.size(); i++){
            int[] range = increasingRanges.get(i);
            while(index <= range[0]) {
                start = start-1; 
                writer.write(Integer.toString(start) + " ");
                index++; 
            }
            while(index <= range[1]){
                writer.write(Integer.toString(start) + " ");
                index++; 
            }
        }
        while(index <= n){
            start = start-1; 
            writer.write(Integer.toString(start) + " ");
            index++; 
        }

        writer.flush(); 
    }

}