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 vasya {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		
		int N = Integer.parseInt(st.nextToken());
		int M = Integer.parseInt(st.nextToken());
		
		int[] array = new int[N + 1];
		array[0] = 10000000;
		State[] info = new State[M];
		
		boolean[] sorts = new boolean[1001];
		
		for (int i = 0; i < M ; i++){
			st = new StringTokenizer(br.readLine());
			info[i] = new State(Integer.parseInt(st.nextToken()), Integer.parseInt(st.nextToken()), Integer.parseInt(st.nextToken()));
			if (info[i].t == 1){
				for (int k = info[i].begin; k < info[i].end; k++){
					sorts[k] = true;
				}
			}
		}
		
		int[] sub = new int[N + 1];
		boolean possible = true;
		
		for (int i = 0; i < M; i++){
			if (info[i].t == 1) continue;
			boolean works = false;
			
			for (int k = info[i].begin; k < info[i].end; k++){
				if (sorts[k] == false){
					sub[k + 1] = 1;
					works = true;
					break;
				}
			}
			if (works == false){
				possible = false;
				System.out.println("NO");
				break;
			}
		}
		if (possible == true){
			System.out.println("YES");
			for (int i = 1; i <= N; i++){
				array[i] = array[i - 1] - sub[i];
				System.out.print(array[i] + " ");
			}
			System.out.println();
		}
		br.close();
	}
	
	static class State implements Comparable<State> {
		public int begin, end, t;
		public State (int a, int b, int c) {
			t = a;
			begin = b;
			end = c;
		}
		public int compareTo (State other) {
			return begin - other.begin;
		}
	}
}