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.StringTokenizer;
import java.util.*;
public class C1187 {
	static class Triplet implements Comparable<Triplet> {
		int s , l,  r;
		public Triplet(int a , int b ,int c) {
			s =a ; l =b ; r = c;
		}
		public int compareTo(Triplet t) {
			return -s + t.s;
		}
		
	}
	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 pair[] = new int[n - 1];
		Triplet [] t = new Triplet[m];
		for (int i = 0; i < m; i++) {
			st = new StringTokenizer(br.readLine());
			int s = Integer.parseInt(st.nextToken());
			int l = Integer.parseInt(st.nextToken()) - 1;
			int r = Integer.parseInt(st.nextToken()) - 1;
			t[i] = new Triplet(s, l, r);
		}
		Arrays.sort(t);
		for(int i = 0 ;i<m;i++) {
			boolean b =false;
			for (int j = t[i].l; j < t[i].r; j++)
				if (t[i].s == 1)
					pair[j] = 1;
				else {
					if (pair[j] != 1) {
						pair[j] = 2;
						b = true;
					}
				}
			if (!b && t[i].s == 0) {
				System.out.println("NO");
				return;
			}
		}
		int[] arr = new int[n];
		arr[0] = 2000;
		for (int i = 1; i < n; i++) {
			if (pair[i - 1] == 2)
				arr[i] = arr[i - 1] - 1;
			else
				arr[i] = arr[i - 1];
		}
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < arr.length; i++)
			sb.append(arr[i] + (i == arr.length - 1 ? "\n" : " "));
		System.out.println("YES");
		System.out.println(sb.toString());
	}

}