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 Solution{
    
    static class Pair implements Comparable<Pair>{
        int l, r;
        Pair(int l, int r){
            this.l = l;
            this.r = r;
        }
        public int compareTo(Pair other){
            if(l != other.l)
                return l-other.l;
            return r-other.r;
        }
    }
    
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        
        int n = sc.nextInt(), m = sc.nextInt(), arr[] = new int[n];
        
        ArrayList<Pair> list = new ArrayList<>(), list2 = new ArrayList<>();
        
        for(int i=0; i<m; i++){
            int t = sc.nextInt(), l = sc.nextInt()-1, r = sc.nextInt()-1;
            
            if(t == 1)
                list.add(new Pair(l, r));
            else
                list2.add(new Pair(l, r));
        }
        
        Collections.sort(list);
        Collections.sort(list2);
        
        arr[0] = 1;
        int index = 0;
        
        for(Pair pair: list){
            int l = pair.l, r = pair.r;
            
            while(index+1 <= l){
                arr[index+1] = arr[index]-1;
                index++;
            }
            
            while(index+1 <= r){
                arr[index+1] = arr[index]+1;
                index++;
            }
        }
        
        while(index+1<n)
        	arr[index+1] = arr[index++]-1;
        	
        //System.out.println(Arrays.toString(arr));
        
        int min = 1;
        for(int q: arr)
            min = Math.min(min, q);
            
        int diff = 1-min;
        boolean flag = true;
    
        outer:for(Pair pair: list2){
            for(int i=pair.l; i<pair.r; i++){
                if(arr[i] > arr[i+1])
                    continue outer;
            }
            System.out.println("NO");
            flag = false;
            break;
        }
        
        if(flag){
            System.out.println("YES");
            for(int i=0; i<n; i++){
                arr[i] = arr[i] + diff;
                System.out.print(+arr[i]+" ");   
            }
        }
    }
}