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 E1187C {

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

        for (int i = 0; i < n; i++) {
            ar[i] = -1000;
        }

        Range[] One = new Range[1000];
        Range[] Non_One = new Range[1000];
        int One_i = 0;
        int Non_One_i = 0;

        for (int i = 0; i < m; i++) {
            int t = sc.nextInt();
            int l = sc.nextInt() - 1;
            int r = sc.nextInt() - 1;
            if (t == 1) {
                One[One_i++] = new Range(l, r);
            } else {
                Non_One[Non_One_i++] = new Range(l, r);
            }
        }
        Arrays.sort(One, 0, One_i, new Range_C());
        Arrays.sort(Non_One, 0, Non_One_i, new Range_C());
        int start_num = 2000;

        for (int i = 0; i < One_i; i++) {
            int s = One[i].start;
            int e = One[i].end;
            if (ar[s] == -1000) {
                ar[s] = start_num;
            }
            for (int j = s + 1; j <= e; j++) {
                if (ar[j] == -1000) {
                    ar[j] = ar[j - 1] + 1;
                }
            }
        }

        int start_num_n = 4000;

        boolean found = false;
        for (int i = 0; i < Non_One_i && !found; i++) {
            int s = Non_One[i].start;
            int e = Non_One[i].end;

            if (ar[s] == -1000) {
                ar[s] = start_num_n;
            }
            int j;
            for (j = s + 1; j <= e; j++) {
                if (ar[j] == -1000) {
                    ar[j] = ar[j - 1] - 1;
                    break;
                } else {
                    if (ar[j] < ar[j - 1]) {
                        break;
                    }
                }
            }
            if (j == e + 1) {
                found = true;
            }
        }
        if (found) {
            System.out.println("NO");
        } else {
            System.out.println("YES");
            for (int i = 0; i < n; i++) {
                if (ar[i] == -1000) {
                    System.out.print(1);
                } else {
                    System.out.print(ar[i]);
                }
                System.out.print(" ");
            }
            System.out.println();
        }
    }
}

class Range_C implements Comparator<Range> {

    public int compare(Range a, Range b) {
        if (a.start != b.start) {
            return a.start - b.start;
        } else {
            return b.end - a.end;
        }
    }
}

class Range {

    int start, end;

    public Range(int s, int e) {
        start = s;
        end = e;
    }
}