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.*;
import java.io.*;

public class C {

    static class FastReader {
        StringTokenizer str;
        BufferedReader br;

        FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            if (str == null || !str.hasMoreTokens()) {
                try {
                    str = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    return "";
                }
            }
            return str.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        char nextChar() {
            return next().charAt(0);
        }

        int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        long[] nextLongArray(int n) {
            long a[] = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }

    static class Pair {
        int start, end;

        Pair (int a, int b) {
            start = a;
            end = b;
        }
    }

    static class Query {
        int t, l, r;

        Query(int a, int b, int c) {
            t = a;
            l = b;
            r = c;
        }

        int gett() {
            return t == 0 ? 1 : 0;
        }

        int getl() {
            return l;
        }

        int getSize() {
            return r - l + 1;
        }
    }

    final static int max = 1000000000;

    public static void main(String args[]) throws Exception {

        FastReader fr = new FastReader();
        int n = fr.nextInt(), m = fr.nextInt();
        ArrayList<Pair> a = new ArrayList<>(m);
        Query queries[] = new Query[m];

        for (int i = 0; i < m; i++)
            queries[i] = new Query(fr.nextInt(), fr.nextInt() - 1, fr.nextInt() - 1);

        Arrays.sort(queries, Comparator.comparing(Query::gett).thenComparing(Query::getl));

        for (int i = 0; i < m; i++) {
            if (queries[i].t == 1) {
                if (a.size() == 0) {
                    a.add(new Pair(queries[i].l, queries[i].r));
                } else {
                    int size = a.size();
                    Pair temp = a.get(size - 1);
                    if (temp.end >= queries[i].l && temp.end < queries[i].r)
                        temp.end = queries[i].r;
                    else if (temp.end < queries[i].l)
                        a.add(new Pair(queries[i].l, queries[i].r));
                }
            } else {
                break;
            }
        }

        for (int i = 0; i < m; i++) {
            if (queries[i].t == 0) {
                for (Pair p : a) {
                    if (p.end >= queries[i].r && p.start <= queries[i].l) {
                        System.out.print("NO");
                        System.exit(0);
                    }
                }
            }
        }

        int ans[] = new int[n];
        ans[0] = max;
        int last = max, pointer = 0;

        for (int i = 0; i < n; i++) {
            if (pointer < a.size()) {
                Pair p = a.get(pointer);
                if (i == p.start) {
                    for (int j = p.start, k = 1; j <= p.end; j++, k++)
                        ans[j] = k;
                    ans[p.end] = max;
                    pointer++;
                    i = p.end;
                    last = max;
                } else {
                    ans[i] = --last;
                }
            } else {
                ans[i] = --last;
            }
        }

        System.out.println("YES");
        for (int i = 0; i < n; i++)
            System.out.print(ans[i] + " ");
    }
}