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 er67c2 {
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt(), q=scan.nextInt();
		int[] a=new int[n];
		for(int i=0;i<n;i++) a[i]=i+1;
		query[] x=new query[q];
		boolean[] sorted=new boolean[n];
		for(int i=0;i<q;i++) {
			int t=scan.nextInt(), l=scan.nextInt()-1, r=scan.nextInt()-1;
			x[i]=new query(t,l,r);
			if(t==1) {
				for(int j=l;j<r;j++) sorted[j]=true;
			}
		}
		out:for(int i=0;i<q;i++) {
			if(x[i].t==0) {
				for(int j=x[i].l;j<x[i].r;j++) {
					if(!sorted[j]) continue out;
				}
				System.out.println("NO");
				return;
			}
		}
		System.out.println("YES");

		for(int i=0;i<n-1;i++) {
			if(!sorted[i]) {
				a[i+1]=a[i]-1;
			}
		}
		int min=0;
		for(int i=0;i<n;i++) min=Math.min(min,a[i]);
		for(int i:a) System.out.print((i-min+1)+" ");
	}
	static class query {
		int t,l,r;
		query(int t, int l, int r) {
			this.t=t;
			this.l=l;
			this.r=r;
		}
	}
}
/*
5 5
0 1 5
0 1 3
0 1 2
0 3 4
0 4 5

10 3
1 2 6
1 4 8
0 3 7
 */