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 Solution {
	static Scanner sc=new Scanner(System.in);
	static PrintWriter out=new PrintWriter(System.out);
	//debug
	static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
	//Main
	public static void main(String args[]) {
		int test=1;
		//test=sc.nextInt();
		while(test-->0) {
			//Think before code, it won't hurt
			int n=sc.nextInt(),m=sc.nextInt(),a[]=new int[n];
			Arrays.fill(a, -1);
			ArrayList<int[]> queries=new ArrayList<>();
			for(int i=0;i<m;i++) {
				int t=sc.nextInt(),l=sc.nextInt()-1,r=sc.nextInt()-1;
				if(t==1) {
					for(int j=l+1;j<=r;j++) a[j]=0;
				}
				else queries.add(new int[] {l+1,r});
			}
			int f=0;
			for(int q[]: queries) {
				int ok=0;
				for(int i=q[0];i<=q[1];i++) {
					if(a[i]==-1) ok=1;
				}
				if(ok==0) f=1;
			}
			if(f==1) {
				out.println("NO");
				continue;
			}
			out.println("YES");
			int cur=1,ans[]=new int[n];
			for(int i=n-1;i>=0;i--) {
				ans[i]=cur;
				if(a[i]==-1) cur++;
			}
			for(int x: ans) out.print(x+" ");
		}
		out.flush();
		out.close();
	}
}