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.ArrayList;
import java.util.Scanner;

public class Codeforces {
    public static void main(String[] args){
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        int m = input.nextInt();
        boolean[] inc = new boolean[n];
        ArrayList<int[]> nonincreas = new ArrayList<>();
        for (int i = 0; i < m; i++){
            if (input.nextInt() == 1){
                int[] k = new int[]{input.nextInt() - 1, input.nextInt() - 1};
                for (int j = k[0]; j < k[1]; j++){
                    inc[j] = true;
                }
            }else{
                nonincreas.add(new int[]{input.nextInt() - 1, input.nextInt() - 1});
            }
        }
        StringBuilder sb = new StringBuilder();
        boolean vanee = true;
        int[] ans = new int[n];
        for (int[] item : nonincreas){
            boolean vane = false;
            for (int i = item[0]; i < item[1]; i++) vane = vane || !inc[i];
            if (!vane) vanee = false;
        }
        if (!vanee) System.out.println("NO");
        else{
            System.out.println("YES");
            ans[0] = 10000;
            for (int i = 1; i < n; i++){
                if (inc[i - 1]) ans[i] = ans[i - 1] + 1;
                else ans[i] = ans[i - 1] - 1;
            }
            for (int x : ans) sb.append(x + " ");
            System.out.println(sb);
        } 
    }
}