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.*;

public class CF1187C {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();

        // 两数之间的排序状态：0-降序，1-升序
        int[] sort_index = new int[n - 1];

        // 非升序区间
        List<String> no_sorted = new ArrayList<>();

        for(int i = 0; i < m; i++){
            int t = sc.nextInt();
            int l = sc.nextInt();
            int r = sc.nextInt();

            if(t == 1){
                setSortIndex(sort_index, l, r);
            }else{
                no_sorted.add(l + "," + r);
            }
        }

        boolean has_solution = true;
        for(int i = 0; i < no_sorted.size(); i++){
            String[] range = no_sorted.get(i).split(",");
            int l = Integer.parseInt(range[0]);
            int r = Integer.parseInt(range[1]);
            if(!checkNoSort(sort_index, l, r)){
                has_solution = false;
                break;
            }
        }

        if(has_solution){
            System.out.println("YES");
            printArray(sort_index);
        }else{
            System.out.println("NO");
        }


    }

    private static void setSortIndex(int[] sort_index, int l, int r){
        for(int i = l - 1; i <= r - 2; i++){
            sort_index[i] = 1;
        }
    }

    private static boolean checkNoSort(int[] sort_index, int l, int r){
        for(int i = l - 1; i <= r - 2; i++){
            if(sort_index[i] == 0){
                return true;
            }
        }
        return false;
    }

    private static void printArray(int[] sort_index){
        int former = 2000;
        StringBuffer sb = new StringBuffer(former + "");
        for(int i = 0; i < sort_index.length; i++){
            if(sort_index[i] == 1){
                sb.append(" ").append(++former);
            }else{
                sb.append(" ").append(--former);
            }
        }
        System.out.println(sb.toString());
    }
}