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.ArrayList;
import java.util.StringTokenizer;

public class C_VasyaAndArray {
    static 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;
        }
    }
    int mod = 1000000007;
    static class Pair{
        int l,r;
        public Pair(int a, int b){
            l=a;
            r=b;
        }
    }

    public static void main(String[] args)throws IOException{
        FastReader fr = new FastReader();
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int n = fr.nextInt();
        int m = fr.nextInt();
        ArrayList<Pair> one = new ArrayList<>();
        ArrayList<Pair> zero = new ArrayList<>();
        for(int i=0;i<m;i++){
            if(fr.nextInt()==1){
                one.add(new Pair(fr.nextInt(),fr.nextInt()));
            }
            else{
                zero.add(new Pair(fr.nextInt(),fr.nextInt()));
            }
        }

        int[] arr = new int[n+1];
        int j;
        for(int i=0;i<one.size();i++){
            j = one.get(i).l+1;
            while (j<=one.get(i).r){
                arr[j]=1;
                j++;
            }
        }
        boolean flag=true;
        for(int i=0;i<zero.size();i++){
            int l = zero.get(i).l;
            int r = zero.get(i).r;
            flag=false;
            for(j=l+1;j<=r;j++){
                if(arr[j]!=1){
                    flag=true;
                    arr[j]=-1;
                    break;
                }
            }
            if(!flag){
                bw.write("NO\n");
                break;
            }
        }
        if(flag){
            bw.write("YES\n");
            int curr=50000;
            for(int i=1;i<=n;i++){
                curr +=arr[i];
                bw.write(curr+" ");
            }
            bw.write("\n");
        }
        bw.flush();
//        if(validate(arr,one,zero)){
//            bw.write("YES\n");
//            arr[0] =500;
//            int cur=500;
//            for(int i=1;i<=n;i++){
////                cur +=arr[i];
//                bw.write(cur+arr[i]+" ");
//            }
//            bw.write("\n");
//        }
//        else{
//            bw.write("NO\n");
//        }
//        bw.flush();
    }

    public static boolean check(Pair i, Pair j){
        if(i.l<=j.l && i.r>=j.r){
            return true;
        }
        return false;
    }

    public static boolean checkall(ArrayList<Pair> one, Pair j){
        for(int i=0;i<one.size();i++){
            if(check(one.get(i),j)){
                return true;
            }
        }
        return false;
    }

    public static boolean validate(int[] arr,ArrayList<Pair> one, ArrayList<Pair> zero){
        for(int i=0;i<zero.size();i++){
            if(checkall(one,zero.get(i))){
                return false;
            }
            for(int j=zero.get(i).l;j<=zero.get(i).r;j++){
                if(arr[j]!=1 && j!=0){
                    arr[j]=-1;
//                    arr[j-1]++;
                    break;
                }
            }
        }
        return true;
    }
}