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.List;
import java.util.Scanner;

public class Main {

    static class Constraint {
        int l, r;

        public Constraint(int l, int r) {
            this.l = l;
            this.r = r;
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        List<Constraint> sorted = new ArrayList<>();
        List<Constraint> notSorted = new ArrayList<>();

        for (int fact = 0; fact < m; fact++) {
            int t = sc.nextInt();
            int l = sc.nextInt() - 1;
            int r = sc.nextInt() - 1;

            if (t == 0) notSorted.add(new Constraint(l, r));
            else sorted.add(new Constraint(l, r));
        }

        int[] sortedFrom = new int[n];
        for (int i = 0; i < n; i++) sortedFrom[i] = i;


        for (Constraint c : sorted) {
            for (int i = c.l; i <= c.r; i++) sortedFrom[i] = Math.min(sortedFrom[i], c.l);
        }

        boolean[] less = new boolean[n];
        for (Constraint c : notSorted) {
            boolean possible = false;
            for (int i = c.l + 1; i <= c.r; i++) {
                if (sortedFrom[i] == i) {
                    less[i] = true;
                    possible = true;
                }
            }

            if (!possible) {
                System.out.println("NO");
                return;
            }
        }

        int[] a = new int[n];
        for (int i = 1; i < n; i++) {
            if (less[i]) a[i] = a[i - 1] - 1;
            else a[i] = a[i - 1] + 1;
        }

        int min = Integer.MAX_VALUE;
        for (int i = 0; i < n; i++) min = Math.min(a[i], min);

        System.out.println("YES");
        for (int i = 0; i < n; i++) {
            System.out.print((a[i] - min + 1) + " ");
        }
    }
}