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.*;
 
public class vasyaAndArray {
 
	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
		int m = scn.nextInt();
		int[][] array = new int[m][3];
		int[] yn = new int[n];
		int[] ans = new int[n];
		for (int i = 0; i < m; i++) {
			array[i][0] = scn.nextInt();
			array[i][1] = scn.nextInt();
			array[i][2] = scn.nextInt() - 1;
		}
		for (int i = 0; i < m; i++) {
			if(array[i][0]==1) {
				
			int l = array[i][1];
			int r = array[i][2];
			for (int j = l; j <= r; j++) {
				yn[j] = 1;
			}
			}
		}
		for (int i = 0; i < m; i++) {
			if(array[i][0]==0)
			{
			boolean flag = false;
			int l = array[i][1];
			int r = array[i][2];
			for (int j = l; j <= r; j++) {
				if (yn[j] != 1) {
					flag = true;
					yn[j] = 2;
				}
			}
			if (!flag) {
				System.out.println("no");
				return;
			}
			}
		}
		
		ans[0]=n;
		
		System.out.println("yes");
		System.out.print(ans[0]+" ");
		for (int i = 1; i <n; i++) {
			if(yn[i]==1) {
				ans[i]=ans[i-1];
				System.out.print(ans[i]+" ");
			}	
			else {
				ans[i]=ans[i-1]-1;
				System.out.print(ans[i]+" ");
			}
				
		}
	}
}