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:

//When I wrote this code, only God & I understood what it did. Now only God knows !!


import java.util.*;
import java.io.*;
import java.math.*;
public class Main {


    static class FastReader
    {
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public FastReader() { this(System.in); }public FastReader(InputStream is) { mIs = is;}
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];}
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;}
        public String next(){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 long l(){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 int i(){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 double d() throws IOException {return Double.parseDouble(next()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; }
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; }
        public void scanIntArr(int [] arr){ for(int li=0;li<arr.length;++li){ arr[li]=i();}}
        public void scanLongArr(long [] arr){for (int i=0;i<arr.length;++i){arr[i]=l();}}
        public void shuffle(int [] arr){ for(int i=arr.length;i>0;--i) { int r=(int)(Math.random()*i); int temp=arr[i-1]; arr[i-1]=arr[r]; arr[r]=temp; } }
    }

    public static int mod = (int) (1e9 + 7);
    public static void main(String[] args) throws IOException {

        FastReader fr = new FastReader();
        PrintWriter pw = new PrintWriter(System.out);
        /*
inputCopy
7 4
1 1 3
1 2 5
0 5 6
1 6 7
outputCopy
YES
1 2 2 3 5 4 4
inputCopy
4 2
1 1 4
0 2 3
outputCopy
NO
      */
        int n=fr.i();
        int m=fr.i();
        boolean [] increasing=new boolean[n];
        boolean [] isSorted=new boolean[n];
        Arrays.fill(isSorted,true);
        int [] ans=new int[n];
        for(int i=0;i<n;++i)
        {
            ans[i]=(i+1)*1000;
        }
        PriorityQueue<Node> pq=new PriorityQueue<Node>();
        for(int mi=0;mi<m;++mi)
        {
            Node node=new Node(fr.i(),fr.i()-1,fr.i()-1);
            pq.add(node);
        }
        boolean possible=true;
        while(!pq.isEmpty())
        {
            Node node=pq.remove();
            if(node.t==1)
            {
                //System.err.println("Here"+node.l+" "+node.r);
                int l=node.l;
                int r=node.r;
                for(int i=l+1;i<=r;++i)
                    increasing[i]=true;
            }
            else
            {
                int l=node.l;
                int r=node.r;
                boolean found=false;
                for(int i=l+1;i<=r;++i)
                {
                    //System.err.println("i="+i+" l"+l+"r="+r+"t="+node.t+" "+Arrays.toString(increasing)+" "+Arrays.toString(isSorted));
                    if(!isSorted[i] || !increasing[i])
                    {
                        //System.err.println("Here 2");
                        ans[i]=ans[i-1]-1;
                        found=true;
                        isSorted[i]=false;
                        break;
                    }
                }
                if(!found)
                {
                    possible=false;
                    break;
                }
            }
        }
        if(!possible)
            pw.println("NO");
        else
        {
            //System.err.println(Arrays.toString(increasing)+" "+Arrays.toString(isSorted));
            pw.println("YES");
            for(int i=0;i<n;++i)
                pw.print(ans[i]+" ");
            pw.println();
        }
        pw.flush();
        pw.close();
    }
    static class Node implements Comparable<Node>
    {
        int t,l,r;

        public Node(int t, int l, int r) {
            this.t = t;
            this.l = l;
            this.r = r;
        }

        public int compareTo(Node other)
        {
            if(this.t==other.t)
                return Integer.compare(this.l,other.l);
            if(this.t==1)
                return -1;
            return 1;

        }

    }
}