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.*;
import java.util.*;
public class C {
	
	static class Query implements Comparable<Query> {
		int left;
		int right;
		
		public Query(int l, int r) {
			left = l;
			right = r;
		}
		
		public int compareTo(Query q) {
			return left - q.left;
		}
	}
	
	public static void main(String[] args) {
		InputReader in = new InputReader();
		int n = in.nextInt();
		int m = in.nextInt();
		
		PriorityQueue<Query> pq = new PriorityQueue<>();
		ArrayList<Query> list = new ArrayList<>();
		for (int i=0; i<m; i++) {
			int type = in.nextInt();
			Query q = new Query(in.nextInt(), in.nextInt());
			if (type == 1)
				pq.add(q);
			else
				list.add(q);
		}
		
		int right = 1;
		int[] arr = new int[n+1];
		while (!pq.isEmpty()) {
			Query q = pq.poll();
			if (q.left > right) {
				for (int i=right+1; i<=q.left; i++)
					arr[i] = 1;
			}
			right = Math.max(right, q.right);
		}
		for (int i=right+1; i<=n; i++) {
			arr[i] = 1;
		}
		
		Collections.sort(list);
		for (Query q: list) {
			boolean good = false;
			for (int i=q.left+1; i<=q.right; i++) {
				if (arr[i] == 1 || arr[i] == -1) {
					arr[i] = -1;
					good = true;
					break;
				}
			}
			if (!good) {
				System.out.println("NO");
				System.exit(0);
			}
		}
		
		StringBuffer sb = new StringBuffer();
		sb.append("YES\n");
		int num = 2000;
		for (int i=1; i<=n; i++) {
			if (arr[i] == -1)
				--num;
			sb.append(num + " ");
		}
		
		System.out.println(sb);
	}

	static class InputReader {
		public BufferedReader br;
		public StringTokenizer st;
		
		public InputReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
			st = null;
		}
		
		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				}
				catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return st.nextToken();
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
}