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.Scanner;

public class Eduactional_Round_67_Problem_C {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int m = sc.nextInt();
		
		int a[] = new int[1001];
		int is_sorted[] = new int[1001];
		int l[] = new int[1001];
		int r[] = new int[1001];
		int c[] = new int[1001];
		
		for(int i = 1; i <= m ; i++)
		{
			is_sorted[i] = sc.nextInt();
			l[i] = sc.nextInt();
			r[i] = sc.nextInt();
			
			if(is_sorted[i] == 1)
			{
				for(int j = l[i]; j < r[i]; j++)
				{
					c[j] = 1;
				}
			}
		}
		
		sc.close();
		
		int startVal = 1000000000 - 2000;
		
		a[1] = startVal;
		
		for(int i = 2; i <= n; i++)
		{
			if(c[i-1] != 1)
				startVal -= 2000;
			a[i] = i + startVal;
			
		}
		
		for(int i = 1; i <= m; i++)
		{
			int pos = 1;
			
			for(int j = l[i]; j < r[i]; j++)
			{
				if(a[j] > a[j+1])
					pos 	= 0;
			}
			if(is_sorted[i] != pos)
				{
					System.out.println("NO");
					return;
				}
		}
		
		System.out.println("YES");
		
		for(int i = 1; i <= n; i++)
		{
			System.out.print(a[i] + " ");
		}
		
		
		
		
	}

}