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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Vector;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Comparator;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author xwchen
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            Vector<Segment> order = new Vector<>();
            Vector<Segment> nonOrder = new Vector<>();
            for (int i = 0; i < m; ++i) {
                int t = in.nextInt();
                int l = in.nextInt();
                int r = in.nextInt();
                if (t == 1) {
                    order.add(new Segment(l, r));
                } else {
                    nonOrder.add(new Segment(l, r));
                }
            }
            Collections.sort(order, Comparator.comparingInt(x -> x.l));
            Vector<Segment> mergedOrder = new Vector<>();
            for (int i = 0; i < order.size(); ) {
                int right = order.get(i).r;
                int left = order.get(i).l;
                int j = i + 1;
                while (j < order.size() && order.get(j).l <= right) {
                    right = Math.max(right, order.get(j).r);
                    ++j;
                }
                i = j;
                mergedOrder.add(new Segment(left, right));
                //System.out.println(left+" -> "+right);
            }

            boolean illegal = false;
            for (Segment mergedorder : mergedOrder) {
                illegal = false;
                for (Segment nonorder : nonOrder) {
                    if (mergedorder.l <= nonorder.l && nonorder.r <= mergedorder.r) {
                        illegal = true;
                        break;
                    }
                }
                if (illegal) {
                    break;
                }
            }
            Collections.sort(mergedOrder, Comparator.comparingInt(x -> x.l));
            if (!illegal) {
                out.println("YES");
                int k = 0;
                int[] a = new int[n];
                int cur = 1000000000;
                for (int i = 0; i < n; ) {
                    int j = i;
                    if (k < mergedOrder.size()) {
                        int orderLeft = mergedOrder.get(k).l;
                        int orderRight = mergedOrder.get(k).r;
                        if (orderLeft <= j + 1 && j + 1 <= orderRight) {
                            while (j < n && orderLeft <= j + 1 && j + 1 <= orderRight) {
                                a[j] = cur;
                                ++j;
                            }
                            ++k;
                            --cur;
                        } else {
                            a[j++] = cur;
                            --cur;
                        }
                    } else {
                        a[j++] = cur;
                        --cur;
                    }
                    i = j;

                }
                for (int i = 0; i < n; ++i) {
                    out.print(a[i] + " ");
                }
            } else {
                out.println("NO");
            }
        }

        class Segment {
            int l;
            int r;

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

        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public InputReader(InputStream inputStream) {
            this.reader = new BufferedReader(
                    new InputStreamReader(inputStream));
        }

        public String next() {
            while (!tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}