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 VasyaAndArray {
    static class pair implements Comparable<pair>{
        int s, e, type;
        public pair(int a, int b, int c){
            s = b;
            e = c;
            type = a;
        }

        @Override
        public int compareTo(pair o) {
            if(this.s == o.s){
                return o.e - this.e;
            }
            return this.s - o.s;
        }
        
    }
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt(); 
        pair[] arr = new pair[m];
        for (int i = 0; i < m; i++) {
            arr[i] = new pair(in.nextInt(), in.nextInt(), in.nextInt());
        }
        Arrays.sort(arr);
        int ans[] = new int[n];
        for (int i = 0; i < m; i++) {
            if(arr[i].type == 1){
                for (int j = arr[i].e - 1; j >= arr[i].s; j--) {
                    if(ans[j] == 1){
                        break;
                    }
                    ans[j] = 1;
                }
            }
        }
        int num = n + 1;
        for (int i = 0; i < n; i++) {
            if(ans[i] == 0){
                ans[i] = --num;
            }else{
                ans[i] = num;
            }
        }
        for (int i = 0; i < m; i++) {
            if(arr[i].type == 0){
                int s = arr[i].s - 1;
                int e = arr[i].e - 1;
                if(ans[s] == ans[e]){
                    System.out.println("NO");
                    return;
                }
            }
        }
        System.out.println("YES");
        for (int i = 0; i < n; i++) {
            if(i == n - 1){
                System.out.println(ans[i]);
            }else{
                System.out.print(ans[i] + " ");
            }
        }
    }
}
/*

0 1 2
1 2 3 4
4 5

*/