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.OutputStream;
import java.io.PrintWriter;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;
 
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author aryssoncf
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }
 
    static class TaskC {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            try {
                int n = in.readInt(), m = in.readInt();
                int[] id = ArrayUtils.createOrder(n);
                ArrayUtils.reverse(id);
                MiscUtils.increaseByOne(id);
                int[] t = new int[m], l = new int[m], r = new int[m];
                in.readIntArrays(t, l, r);
                MiscUtils.decreaseByOne(l, r);
                for (int i = 0; i < m; i++) {
                    if (t[i] == 1) {
                        int label = id[r[i]], old = id[l[i]];
                        for (int j = r[i] - 1; j >= 0 && id[j] <= old; j--) {
                            id[j] = label;
                        }
                    }
                }
                boolean valid = true;
                for (int i = 0; i < m; i++) {
                    if (t[i] == 0) {
                        if (id[l[i]] == id[r[i]]) {
                            valid = false;
                        }
                    }
                }
                if (valid) {
                    out.printLine("YES");
                    out.printLine(id);
                } else {
                    out.printLine("NO");
                }
            } catch (Exception e) {
                e.printStackTrace();
            }
        }
 
    }
 
    static interface IntReversableCollection extends IntCollection {
    }
 
    static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
        IntIterator intIterator();
 
        default Iterator<Integer> iterator() {
            return new Iterator<Integer>() {
                private IntIterator it = intIterator();
 
                public boolean hasNext() {
                    return it.isValid();
                }
 
                public Integer next() {
                    int result = it.value();
                    it.advance();
                    return result;
                }
            };
        }
 
        default int compareTo(IntStream c) {
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                int i = it.value();
                int j = jt.value();
                if (i < j) {
                    return -1;
                } else if (i > j) {
                    return 1;
                }
                it.advance();
                jt.advance();
            }
            if (it.isValid()) {
                return 1;
            }
            if (jt.isValid()) {
                return -1;
            }
            return 0;
        }
 
    }
 
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
 
        public void readIntArrays(int[]... arrays) {
            for (int i = 0; i < arrays[0].length; i++) {
                for (int j = 0; j < arrays.length; j++) {
                    arrays[j][i] = readInt();
                }
            }
        }
 
        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 readInt() {
            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 {
            boolean isSpaceChar(int ch);
 
        }
 
    }
 
    static interface IntList extends IntReversableCollection {
        public abstract int get(int index);
 
        public abstract void set(int index, int value);
 
        public abstract void removeAt(int index);
 
        default public void swap(int first, int second) {
            if (first == second) {
                return;
            }
            int temp = get(first);
            set(first, get(second));
            set(second, temp);
        }
 
        default public IntIterator intIterator() {
            return new IntIterator() {
                private int at;
                private boolean removed;
 
                public int value() {
                    if (removed) {
                        throw new IllegalStateException();
                    }
                    return get(at);
                }
 
                public boolean advance() {
                    at++;
                    removed = false;
                    return isValid();
                }
 
                public boolean isValid() {
                    return !removed && at < size();
                }
 
                public void remove() {
                    removeAt(at);
                    at--;
                    removed = true;
                }
            };
        }
 
        default public void inPlaceReverse() {
            for (int i = 0, j = size() - 1; i < j; i++, j--) {
                swap(i, j);
            }
        }
 
    }
 
    static interface IntIterator {
        public int value() throws NoSuchElementException;
 
        public boolean advance();
 
        public boolean isValid();
 
    }
 
    static class Range {
        public static IntList range(int from, int to) {
            int[] result = new int[Math.abs(from - to)];
            int current = from;
            if (from <= to) {
                for (int i = 0; i < result.length; i++) {
                    result[i] = current++;
                }
            } else {
                for (int i = 0; i < result.length; i++) {
                    result[i] = current--;
                }
            }
            return new IntArray(result);
        }
 
    }
 
    static interface IntCollection extends IntStream {
        public int size();
 
        default public int[] toArray() {
            int size = size();
            int[] array = new int[size];
            int i = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                array[i++] = it.value();
            }
            return array;
        }
 
    }
 
    static class ArrayUtils {
        public static int[] range(int from, int to) {
            return Range.range(from, to).toArray();
        }
 
        public static int[] createOrder(int size) {
            return range(0, size);
        }
 
        public static void reverse(int[] array) {
            new IntArray(array).inPlaceReverse();
        }
 
    }
 
    static class OutputWriter {
        private final PrintWriter writer;
 
        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
 
        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }
 
        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }
 
        public void print(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }
 
        public void printLine(int[] array) {
            print(array);
            writer.println();
        }
 
        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }
 
        public void close() {
            writer.close();
        }
 
    }
 
    static class IntArray extends IntAbstractStream implements IntList {
        private int[] data;
 
        public IntArray(int[] arr) {
            data = arr;
        }
 
        public int size() {
            return data.length;
        }
 
        public int get(int at) {
            return data[at];
        }
 
        public void removeAt(int index) {
            throw new UnsupportedOperationException();
        }
 
        public void set(int index, int value) {
            data[index] = value;
        }
 
    }
 
    static class MiscUtils {
        public static void decreaseByOne(int[]... arrays) {
            for (int[] array : arrays) {
                for (int i = 0; i < array.length; i++) {
                    array[i]--;
                }
            }
        }
 
        public static void increaseByOne(int[]... arrays) {
            for (int[] array : arrays) {
                for (int i = 0; i < array.length; i++) {
                    array[i]++;
                }
            }
        }
 
    }
 
    static abstract class IntAbstractStream implements IntStream {
        public String toString() {
            StringBuilder builder = new StringBuilder();
            boolean first = true;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                if (first) {
                    first = false;
                } else {
                    builder.append(' ');
                }
                builder.append(it.value());
            }
            return builder.toString();
        }
 
        public boolean equals(Object o) {
            if (!(o instanceof IntStream)) {
                return false;
            }
            IntStream c = (IntStream) o;
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                if (it.value() != jt.value()) {
                    return false;
                }
                it.advance();
                jt.advance();
            }
            return !it.isValid() && !jt.isValid();
        }
 
        public int hashCode() {
            int result = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                result *= 31;
                result += it.value();
            }
            return result;
        }
 
    }
}