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.awt.*;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.Scanner;
import java.util.*;

public class CF_1187C {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintStream out = System.out;

        int N = in.nextInt(), M = in.nextInt();

        ArrayList<Point> constraints = new ArrayList<>();
        int[] lp = new int[N + 1];
        for(int i = 0; i < M; i++){
            if(in.nextInt() == 0) {
                constraints.add(new Point(in.nextInt() - 1, in.nextInt() - 1));
            }else{
                lp[in.nextInt()]++;
                lp[in.nextInt()]--;
            }
        }

        int[] ret = new int[N];
        int curr = 0;
        int currVal = 1000000000;
        for(int i = 0; i < N; i++){
            curr += lp[i];
            if(curr > 0){
                ret[i] = currVal;
            }else{
                ret[i] = --currVal;
            }
        }

        boolean valid = true;
        for(Point p: constraints){
            for(int i = p.x; i < p.y; i++){
                if(ret[i+1] < ret[i]){
                    break;
                }
                if(i == p.y - 1) valid = false;
            }
        }

        if(valid){
            out.println("YES");
            for(int i: ret){
                out.print(i + " ");
            }
        }else{
            out.println("NO");
        }

        out.close();
        in.close();
    }
}