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.math.*;
import java.text.*;
import java.util.*;
import java.util.regex.*;

public class Solution 
{
    public static void main(String[] args) throws Exception 
    {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter w = new PrintWriter(System.out);
        String[] s1 = in.readLine().trim().split("\\s+");
        int n = Integer.parseInt(s1[0]);
        int m = Integer.parseInt(s1[1]);
        int[][] ref = new int[m][3];
        boolean gpos = true;
        ArrayList<Integer> al = new ArrayList<Integer>();
        int[] available = new int[n+1];
        for(int q=0;q<m;q++)
        {
            String[] s2 = in.readLine().trim().split("\\s+");
            int t = Integer.parseInt(s2[0]);
            int l = Integer.parseInt(s2[1]);
            int r = Integer.parseInt(s2[2]);
            ref[q][0] = t;
            ref[q][1] = l-1;
            ref[q][2] = r-1;
            if(ref[q][0]==1)
            {
                available[ref[q][1]]+=1;
                available[ref[q][2]]-=1;
            }
        }
        for(int i=1;i<=n;i++)
        {
            available[i] += available[i-1];
            // w.print(available[i-1]+" ");
        }
        // w.println();
        for(int p=0;p<m;p++)
        {
            int t = ref[p][0];
            int l = ref[p][1];
            int r = ref[p][2];
            if(t==0)
            {
                boolean pos = false;
                for(int i=l;i<r;i++)
                {
                    if(available[i] <= 0)
                    {
                        pos = true;
                        al.add(i);
                        break;
                    }
                }
                gpos = gpos&pos;
                if(!gpos)
                    break;
            }
        }
        if(gpos)
        {
            w.println("YES");
            int[] ans = new int[n];
            int cur = al.size();
            Collections.sort(al);
            int prev = -1;
            for(int i=0;i<al.size();i++)
            {
                if(al.get(i)==prev)
                    continue;
                prev = al.get(i);
                ans[al.get(i)]+=cur;
                cur--;
            }
            for(int i=0;i<n;i++)
            {
                w.print((ans[i]+1)+" ");
            }
            w.println();
        }
        else
            w.println("NO");
        w.close();
    }
}