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:
//package vasyaandarray;

import java.util.*;
import java.io.*;

public class vasyaandarray {
	public static void main(String[] args) throws IOException {
		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(fin.readLine());
		int n = Integer.parseInt(st.nextToken());
		int m = Integer.parseInt(st.nextToken());
		int[] pfx = new int[n * 2 + 1];
		int[] pfxUnsorted = new int[n * 2 + 1];
		ArrayList<int[]> unsorted = new ArrayList<int[]>();
		for(int i = 0; i < m; i++) {
			st = new StringTokenizer(fin.readLine());
			int which = Integer.parseInt(st.nextToken());
			int l = (Integer.parseInt(st.nextToken()) - 1) * 2 + 1;
			int r = (Integer.parseInt(st.nextToken()) - 1) * 2;
			if(which == 1) {
				pfx[l] += 1;
				if(r != n * 2) {
					pfx[r + 2] += -1;
				}
				else {
					//System.out.println("FAOL " + i);
				}
			}
			else {
				unsorted.add(new int[] {l, r});
			}
//			for(int j : pfx) {
//				System.out.print(j + " ");
//			}
//			System.out.println();
		}
		
		for(int i = 0; i < pfx.length - 1; i++) {
			pfx[i + 1] += pfx[i];
			pfxUnsorted[i + 1] += pfxUnsorted[i] + (pfx[i] == 0? 1 : 0);
		}
//		for(int i : pfxUnsorted) {
//			System.out.print(i + " ");
//		}
//		System.out.println();
		int pointer = 1000000;
		StringBuilder fout = new StringBuilder();
		for(int i = 1; i < pfx.length; i += 2) {
			if(pfx[i - 1] == 0) {
				pointer --;
			}
			else {
				pointer ++;
			}
			fout.append(pointer).append(" ");
		}
		boolean isValid = true;
		for(int i = 0; i < unsorted.size(); i++) {
			int[] next = unsorted.get(i);
			int l = next[0];
			int r = next[1] + 1;
			if(pfxUnsorted[l] == pfxUnsorted[r]) {
				isValid = false;
				break;
			}
		}
		if(isValid) {
			System.out.println("YES\n" + fout);
		}
		else {
			System.out.println("NO");
		}
	}
}