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.math.*;
import java.io.*;

/* abhi2601 */

public class Q1 implements Runnable{

    final static long mod = (long)1e9 + 7;
    static class Pair implements Comparable<Pair>{
        int a;
        int b;
        Pair(int a,int b){
            this.a=a;
            this.b=b;
        }
        public int compareTo(Pair p){
            if(this.a-p.a==0) return this.b-p.b;
            return this.a-p.a;
        }
    }
    public void run(){
        InputReader sc = new InputReader(System.in);
        //BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter w = new PrintWriter(System.out);
        int n=sc.nextInt();
        int m=sc.nextInt();
        ArrayList<Pair>a1=new ArrayList<>();
        ArrayList<Pair>a0=new ArrayList<>();
        int ans[]=new int[n+1];
        ans[0]=2*n;
        for(int i=1;i<=n;i++) ans[i]=ans[i-1]-1;
        for(int i=0;i<m;i++){
            int q=sc.nextInt();
            if(q==1) a1.add(new Pair(sc.nextInt(),sc.nextInt()));
            else a0.add(new Pair(sc.nextInt(),sc.nextInt()));
        }
        Collections.sort(a1);
        Collections.sort(a0);
        ArrayList<Pair>fa1=new ArrayList<>();
        if(a1.size()!=0) fa1.add(a1.get(0));
        for(int i=1;i<a1.size();i++){
            if(a1.get(i).a<=fa1.get(fa1.size()-1).b) fa1.get(fa1.size()-1).b=Math.max(fa1.get(fa1.size()-1).b,a1.get(i).b);
            else fa1.add(a1.get(i));
        }
        for(int i=0;i<fa1.size();i++){
            int l=fa1.get(i).a+1;
            int r=fa1.get(i).b;
            for(int j=l;j<=r;j++) ans[j]=ans[fa1.get(i).a];
        }
        //for(int i=1;i<=n;i++) w.print(ans[i]+" ");
        int z=0;
        for(int i=0;i<a0.size();i++){
            int l=a0.get(i).a;
            int r=a0.get(i).b;
            int c=0;
            for(int j=l;j<r;j++){
                if(ans[j]>ans[j+1]){
                    c++;
                    break;
                }
            }
            if(c==0){
                w.println("NO");
                z++;
                break;
            }
        }
        if(z==0){
            w.println("YES");
            for(int i=1;i<=n;i++) w.print(ans[i]+" ");
        }
        w.close();
    }
    static class Comp implements Comparator<String>{
        public int compare(String x,String y){
            if(x.length()-y.length()==0){
                return x.compareTo(y);
            }
            return x.length()-y.length();
        }
    }
    //static PrintWriter w;
    /*File in=new File("input.txt");
        File out=new File("output.txt");
        Scanner sc= null;
        try {
            sc = new Scanner(in);
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
        try {
            w=new PrintWriter(out);
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }*/
    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int read()
        {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars)
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine()
        {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt()
        {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-')
            {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do
            {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next()
        {
            return readString();
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception
    {
        new Thread(null, new Q1(),"q1",1<<26).start();
    }
}