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.Scanner;

public class CFE67C {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        
        int length = scan.nextInt();
        boolean[] nonDecrease = new boolean[length];
        
        int facts = scan.nextInt();
        int decFacts = 0;
        int[][] decFact = new int[facts][2];
        
        for (int i=0; i<facts; i++) {
            if (scan.nextInt() == 1) {
                int j = scan.nextInt()-1;
                int limit = scan.nextInt()-1;
                for (; j<limit; j++) {
                    nonDecrease[j] = true;
                }
            } else {
                decFact[decFacts][0] = scan.nextInt()-1;
                decFact[decFacts++][1] = scan.nextInt()-1;
            }
        }
        
        for (int i=0; i<decFacts; i++) {
            int j = decFact[i][0];
            int limit = decFact[i][1];
            for (; j < limit && nonDecrease[j] == true; j++);
            if (j == limit) {
                System.out.println("NO");
                return;
            }
        }
        
        System.out.println("YES");
        System.out.print(length);
        int last = length;
        int limit = length-1;
        for (int i=0; i<limit; i++) {
            if (!nonDecrease[i]) {
                last--;
            }
            System.out.print(" "+last);
        }
        System.out.println();
    }    
}