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;
import java.util.Vector;

public class C{
	static class Pair{
		int l;
		int r;
		Pair(int l, int r){
			this.l = l;
			this.r = r;
		}
		Pair(Pair p){
			l = p.l;
			r = p.r;
		}
		public String toString(){
			return "(" + l + ", " + r + ")";
		}
	}
	public static Vector<Pair> buildUp(Vector<Pair> up){
		Vector<Pair> res = new Vector<>();
		Pair cur = new Pair(up.get(0));
		for(int i = 0; i< up.size();++i){
			if(up.get(i).l<=cur.r){
				cur.r = Math.max(up.get(i).r, cur.r);
			} else{
				res.add(cur);
				cur = new Pair(up.get(i));
			}
		}
		res.add(cur);
		return res;
	}
	public static boolean check(Vector<Pair> down, Vector<Pair> up){
		for(int i = 0;i < down.size();++i){
			int j = 0;
			while(j < up.size() && up.get(j).l <=down.get(i).l){
				if(up.get(j).l <= down.get(i).l && down.get(i).r <= up.get(j).r) return false;
				j++;
			}
		}
		return true;
	}
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int m = in.nextInt();
		Vector<Pair> up = new Vector<>();
		Vector<Pair> down = new Vector<>();
		for(int i = 0;i<m;++i){
			if(in.nextInt() == 1)
				up.add(new Pair(in.nextInt(), in.nextInt()));
			else down.add(new Pair(in.nextInt(), in.nextInt()));
		}
		up.sort((x,y) -> (x.l == y.l)?Integer.compare(x.r,y.r):Integer.compare(x.l,y.l));
		down.sort((x,y) -> (x.l == y.l)?Integer.compare(x.r,y.r):Integer.compare(x.l,y.l));
		if(up.size() > 0) up = buildUp(up);
		if(!check(down, up)){
			System.out.println("NO");
			return;
		}
		//System.out.println(up);
		StringBuilder res = new StringBuilder().append("YES\n");
		int cur = 1002;
		int it = 0;
		for(int i = 1;i<=n;++i){
			if(it < up.size() && up.get(it).l < i && up.get(it).r>=i){
				res.append(++cur + " ");
				if(i == up.get(it).r) it++;
			} else res.append(--cur + " ");
		}
		System.out.println(res);
	}
}