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.util.*;
import java.lang.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.*;
 
public class Main {
    public static void main(String[] args) throws Exception{
        FastReader sc=new FastReader(); 
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        Main mm=new Main();
        int n=sc.nextInt();
        int[] arr=new int[n];
        int m=sc.nextInt();
        ArrayList<node> one=new ArrayList<node>();
        ArrayList<node> zero=new ArrayList<node>();
        for(int i=0;i<m;i++) {
            int temp=sc.nextInt();
            if(temp==1) {
                one.add(new node(sc.nextInt()-1,sc.nextInt()-1));
            }
            else {
                zero.add(new node(sc.nextInt()-1,sc.nextInt()-1));
            }
        }
        for(int i=0;i<n-1;i++) {
            int flag=1;
            for(node j:one) {
                if(i>=j.l && i+1<=j.r) {
                    flag=0;break;
                }
            }
            if(flag==1) {
                for(int j=i+1;j<n;j++) {
                    arr[j]-=1;
                }
            }
        }
        for(int i=0;i<n;i++) {
            arr[i]+=10000000;
        }
        int flag=1;
        for(node i:one) {
            for(int j=i.l;j<i.r;j++) {
                if(arr[j]>arr[j+1]) {
                    flag=0;
                    break;
                }
            }
            if(flag==0) {
                break;
            }
        }
        for(node i:zero) {
            int f=0;
            for(int j=i.l;j<i.r;j++) {
                if(arr[j]>arr[j+1]) {
                    f=1;
                    break;
                }
            }
            if(f==0) {
                flag=0;
                break;
            }
        }
        if(flag==0) {
            System.out.println("NO");
        }
        else {
            System.out.println("YES");
            for(int i=0;i<n;i++) {
                System.out.print(arr[i]+" ");
            }
        }
    }  
}
class node{
    int l;int r;
    node(int l,int r){
        this.l=l;this.r=r;
    }
}
class b implements Comparator<node>{
    public int compare(node n1,node n2) {
        if(n1.l==n2.l) {
            return n1.r-n2.r;
        }
        else {
            return n1.l-n2.l;
        }
    }
}
class a implements Comparator<node>{
    public int compare(node n1,node n2) {
        if(n1.l==n2.l) {
            return n2.r-n1.r;
        }
        else {
            return n1.l-n2.l;
        }
    }
}
class FastReader 
{ 
    BufferedReader br; 
    StringTokenizer st; 
 
    public FastReader() 
    { 
        br = new BufferedReader(new
                 InputStreamReader(System.in)); 
    } 
 
    String next() 
    { 
        while (st == null || !st.hasMoreElements()) 
        { 
            try
            { 
                st = new StringTokenizer(br.readLine()); 
            } 
            catch (IOException  e) 
            { 
                e.printStackTrace(); 
            } 
        } 
        return st.nextToken(); 
    } 
 
    int nextInt() 
    { 
        return Integer.parseInt(next()); 
    } 
 
    long nextLong() 
    { 
        return Long.parseLong(next()); 
    } 
 
    double nextDouble() 
    { 
        return Double.parseDouble(next()); 
    } 
 
    String nextLine() 
    { 
        String str = ""; 
        try
        { 
            str = br.readLine(); 
        } 
        catch (IOException e) 
        { 
            e.printStackTrace(); 
        } 
        return str; 
    } 
}