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:
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main (String[] args) {
		Scanner input = new Scanner(System.in);
			int n = input.nextInt();
			int m = input.nextInt();
			int[] arr = new int[n+2];
			
			//System.out.print("N " + n + "M " + m);
			
			HashMap<Integer, List<Interval>> facts = new HashMap<>();
			facts.put(1, new ArrayList<>());
			facts.put(0, new ArrayList<>());
			Arrays.fill(arr, 0);
			for(int i = 0; i < m; i++) {
				int type = input.nextInt();
				int start = input.nextInt();
				int end = input.nextInt();
				facts.get(type).add(new Interval(start, end));
			}
			
		    List<Interval> sortedList  = facts.get(1);
			for(int i = 0; i < sortedList.size(); i++) {
				new Ideone().populateArr(arr, sortedList.get(i).start,  sortedList.get(i).end, 1);
			}
			
			List<Interval> unSortedList  = facts.get(0);
			for(int i = 0; i < unSortedList.size(); i++) {
				int count = new Ideone().populateArr(arr, unSortedList.get(i).start,  unSortedList.get(i).end, -1);
				//System.out.println("Count: " + count);
				if(count == 0) {
					System.out.println("NO");
					//System.out.println(unSortedList.get(i).start + "  + " + unSortedList.get(i).end);
					return;
				}
			}
			
			int temp = 1001;
			System.out.println("YES");

			for(int i = 1; i <= n; i++) {
				temp = temp + arr[i];
				System.out.print(temp + " ");
			}
	}
	
	int populateArr(int arr[], int start, int end, int val) {
		int count = 0;
		for(int i = start + 1; i  <= end; i++) {
			if(arr[i] == val || arr[i] == 0) {
				arr[i] = val;
				count++;
			}
		}
		return count;
	}
}

class Interval {
	public int start;
	public int end;
	
	public Interval(int start, int end) {
		this.start = start;
		this.end = end;
	}
}