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.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;

public class C1187 {
	
	private static class Pair implements Comparable<Pair>{
		long first;
		long second;

		Pair(long first, long second) {
			this.first = first;
			this.second = second;
		}

		@Override
		public int compareTo(Pair p) {
			if(first>p.first) return 1;
			else if(first<p.first)return -1;
			else if(second>p.second) return 1;
			else if(second<p.second) return -1;
			return 0;
		}
	}

	public static void main(String[] args) throws Exception {
//		BufferedReader br = new BufferedReader(new FileReader("F:/books/input.txt"));
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] s1 = br.readLine().split(" ");
		ArrayList<Pair> asc = new ArrayList<Pair>();
		ArrayList<Pair> desc = new ArrayList<Pair>();
		ArrayList<Pair> list = new ArrayList<Pair>();
		Integer n = Integer.parseInt(s1[0]);
		Integer m = Integer.parseInt(s1[1]);
		for(int i=0;i<m;i++) {
			String[] s2 = br.readLine().split(" ");
			Integer t = Integer.parseInt(s2[0]);
			Integer l = Integer.parseInt(s2[1]);
			Integer r = Integer.parseInt(s2[2]);
			if(t==0) desc.add(new Pair(l,r));
			else asc.add(new Pair(l,r));
		}
		Collections.sort(asc);
		long l=-10,r=-10;
		for(Pair p : asc) {
			if(p.first<=r) r = Math.max(r, p.second);
			else {
				if(l>0)
					list.add(new Pair(l,r));
				l=p.first;
				r=p.second;
			}
		}
		if(l>0) list.add(new Pair(l,r));
		for(Pair p : desc) {
			int pos = Collections.binarySearch(list, p);
			if(pos>=0) exit();
			pos =-pos-1;
			if(pos<list.size()) 
				if(p.first>=list.get(pos).first && p.second<=list.get(pos).second) exit();
			if(pos>0) 
				if(p.first>=list.get(pos-1).first && p.second<=list.get(pos-1).second) exit();
		}
		int[] a = new int[1001];
		int x=n;
		
		for(int i=1;i<=n;i++) {
			a[i]=x--;
		}
		for(Pair p : list) {
			for (int i = (int) p.first+1; i <= p.second; i++) {
				a[i] = a[i-1];
			}
		}
		StringBuilder sb = new StringBuilder("YES\n");
		for(int i=1;i<=n;i++) sb.append(a[i]+" ");
		System.out.println(sb.toString());
	}
	
	private static void exit() {
		System.out.println("NO");
		System.exit(0);
	}

}