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.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class VasyaAndArray {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int M = in.nextInt();
        int[] arr = new int[N];
        int[][] given = new int[M][3];
        for (int i = 0; i < M; i++) {
            int t = in.nextInt();
            int r = in.nextInt()-1;
            int l = in.nextInt()-1;
            given[i] = new int[]{t, r, l};
        }
        Arrays.sort(given, new Comparator<int[]>() {
            @Override
            public int compare(int[] o1, int[] o2) {
                return Integer.compare(o2[0], o1[0]);
            }
        });
        int pointer = 0;
        int identifier = -1;
        arr[0] = N;
        while (pointer < given.length && given[pointer][0] == 1) {
            for (int i = given[pointer][1]; i < given[pointer][2]; i++) {
                arr[i] = 1;
            }
            identifier--;
            pointer++;
        }
        int[] newarr = new int[N];
        newarr[0] = N;
        for (int i = 1; i < N; i++) {
            newarr[i] = newarr[i-1] + (arr[i-1] == 1 ? 0 : -1);
        }
        while (pointer < given.length && given[pointer][0] == 0) {
            boolean works = false;

            for (int i = given[pointer][1]; i < given[pointer][2]; i++) {
                if (newarr[i] > newarr[i+1]) {
                    works = true;
                }
            }
            if (!works) {
                System.out.println("NO");
                System.exit(0);
            }
            pointer++;
        }
        System.out.println("YES");
        for (int i = 0; i < N; i++) {
            System.out.print(newarr[i] + " ");
        }



    }
}