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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class C {
    final int INF = 1_000_000_000;
    void solve() {
        int n = readInt();
        int m = readInt();
        int[][] a = new int[3][m];
        for(int i = 0;i<m;i++){
            for(int j = 0;j<3;j++){
                a[j][i] = readInt();
            }
        }
        boolean[] bad = new boolean[n];
        bad[0] = true;
        for(int i = 0;i<m;i++){
            if(a[0][i] == 0) continue;
            for(int j = a[1][i];j<a[2][i];j++){
                bad[j] = true;
            }
        }
        for(int i = 0;i<m;i++){
            if(a[0][i] == 1) continue;
            boolean good = false;
            for(int j = a[1][i];j<a[2][i];j++){
                if(!bad[j]) good = true;
            }
            if(!good){
                out.print("NO");
                return;
            }
        }
        int[] res = new int[n];
        int now = 2000;
        for(int i = 0;i<n;i++){
            if(!bad[i]) res[i] = --now;
            else res[i] = now;
        }

        out.println("YES");
        for(int i : res){
            out.print(i + " ");
        }
    }

    public static void main(String[] args) {
        new C().run();
    }

    private void run() {
        try {
            init();
            solve();
            out.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    private BufferedReader in;
    private StringTokenizer tok = new StringTokenizer("");

    private PrintWriter out;

    private void init() {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);

//        try {
//            in = new BufferedReader(new FileReader("absum.in"));
//            out = new PrintWriter(new File("absum.out"));
//        } catch (FileNotFoundException e) {
//            e.printStackTrace();
//        }
    }

    private String readLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    private String readString() {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (nextLine == null) return null;
            tok = new StringTokenizer(nextLine);
        }

        return tok.nextToken();
    }

    private int readInt() {
        return Integer.parseInt(readString());
    }

    private long readLong() {
        return Long.parseLong(readString());
    }
}