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.*;
import java.util.*;

public class Main {



    static class Task {
        static class Line1 {
            int l;
            int r;

            public Line1(int l, int r) {
                this.l = l;
                this.r = r;
            }

            boolean canMergeRight(Line1 rightLine) {
                return rightLine.l <= r && rightLine.r >= l;
            }

            @Override
            public String toString() {
                return "Line1{" +
                        "l=" + l +
                        ", r=" + r +
                        '}';
            }
        }

        class BadLine {
            int l, r;

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

            boolean satisfies(int[] arr) {
                for (int i = l + 1; i <= r; i++) {
                    if (arr[i - 1] > arr[i]) {
                        return true;
                    }
                }

                return false;
            }

            @Override
            public String toString() {
                return "BadLine{" +
                        "l=" + l +
                        ", r=" + r +
                        '}';
            }
        }

        PrintWriter out;
        MyScanner in;

        public void solve(MyScanner in, PrintWriter out) {

            Map<Character, ArrayList<Integer>> charToPosition = new HashMap<>();

            int n = in.nextInt();
            int m = in.nextInt();


            List<Line1> line1s = new ArrayList<>();
            List<BadLine> badLines = new ArrayList<>();


            for (int i = 0; i < m; i++) {
                int t = in.nextInt();
                int l = in.nextInt();
                int r = in.nextInt();

                if (t == 0)  {
                    badLines.add(new BadLine(l, r));
                } else {
                    line1s.add(new Line1(l, r));
                }
            }

            line1s.sort((a, b) -> new Integer(a.l).compareTo(b.l));


           // System.out.println("Pre merge " + line1s);
            int i = 0;
            while (true) {
                while (i + 1 < line1s.size() && line1s.get(i).canMergeRight(line1s.get(i + 1))) {
                    line1s.get(i).r = Math.max(line1s.get(i + 1).r, line1s.get(i).r);
                    line1s.remove(i + 1);
                }
                i++;
                if (i >= line1s.size()) {
                    break;
                }
            }

           // System.out.println("Post merge " + line1s);


            int indLine1 = 0;
            Line1 currentLine = indLine1 < line1s.size() ? line1s.get(indLine1) : null;

            int val = 1_000_000_000;


            int[] arr = new int[n + 1];

            for (i = 1; i <= n; i++) {
                boolean dec = true;

                if (currentLine != null) {
                    if (i <= currentLine.l) {

                    } else if (i <= currentLine.r) {
                        dec = false;
                    } else {
                        indLine1++;
                        currentLine = indLine1 < line1s.size() ? line1s.get(indLine1) : null;
                    }
                }

                if (dec) {
                    val--;
                }

                arr[i] = val;
            }

           // System.out.println(Arrays.toString(arr));


            // check
            boolean isError = false;


           // System.out.println("checking for errors" + badLines);
            for (BadLine badLine: badLines) {
                if (!badLine.satisfies(arr)) {
                    isError = true;
                }
            }

            if (isError) {
                out.println("NO");
            } else {
                out.println("YES");
                for (i = 1; i <= n; i++) {
                    out.print(arr[i] + " ");
                }
                out.println();
            }

        }
    }

    public static void main(String[] args) {
        MyScanner in = new MyScanner();
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}