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.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

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

    static class CVasyaAndArray {
        public void solve(int testNumber, FastScanner br, PrintWriter pw) {
            int n = br.nextInt();
            int m = br.nextInt();
            long[] arr = new long[n];
            ArrayList<Tuple> queries = new ArrayList<>();


            boolean[] need = new boolean[n];
            for (int i = 0; i < m; i++) {
                int qt = br.nextInt();
                int ql = br.nextInt();
                int qr = br.nextInt();
                ql--;
                qr--;
                queries.add(new Tuple(qt, ql, qr));
                if (qt == 1) {
                    for (int j = ql; j < qr; j++) {
                        need[j] = true;
                    }
                }
            }
            int val = (int) 1e9;
            for (int i = 0; i < n - 1; i++) {
//            pw.print(need[i] + " ");
                if (need[i]) {
                    arr[i] = val;
                    arr[i + 1] = val;
                } else {

                    arr[i] = val;
                    arr[i + 1] = val - 1;
                    val--;
                }
            }

            for (int i = 0; i < m; i++) {
                Tuple curr = queries.get(i);
                int a = curr.a;
                int b = curr.b;
                int c = curr.c;
                if (a == 1) {
                    for (int j = b + 1; j <= c; j++) {
                        if (arr[j] > arr[j - 1]) {
                            pw.println("NO");
                            pw.close();
                            return;
                        }
                    }
                } else {
                    boolean works = false;
                    for (int j = b + 1; j <= c; j++) {
                        if (arr[j] < arr[j - 1]) {
                            works = true;
                        }
                    }
                    if (!works) {
                        pw.println("NO");
                        pw.close();
                        return;
                    }
                }
            }
            pw.println("YES");
            for (int i = 0; i < n; i++) {
                pw.print(arr[i] + " ");
            }
            pw.close();
        }

        public class Tuple implements Comparable<Tuple> {
            int a;
            int b;
            int c;

            public Tuple(int a, int b, int c) {
                this.a = a;
                this.b = b;
                this.c = c;
            }

            public int compareTo(Tuple t) {
                if (this.a == t.a && this.b == t.b) {
                    return this.c - t.c;
                } else if (this.a == t.a) {
                    return this.b - t.b;
                } else {
                    return this.a - t.a;
                }
            }

        }

    }

    static class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastScanner.SpaceCharFilter filter;

        public FastScanner(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}