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 {
    void solve() throws FileNotFoundException, IOException {
        int n = ni();
        int k = ni();
        int[] a = new int[n];

        ArrayList<Range> t1 = new ArrayList<>();
        ArrayList<Range> t2 = new ArrayList<>();

        for (int i = 0; i < k; i++) {
            int t = ni();
            if (t == 1) {
                t1.add(new Range(ni() - 1, ni() - 1));
            } else {
                t2.add(new Range(ni()- 1, ni() - 1));
            }
        }

        ArrayList<Action> actions = new ArrayList<>();
        for (Range r: t1) {
            actions.add(new Action(0, r.l));
            actions.add(new Action(1, r.r));
        }
        Collections.sort(actions);

        ArrayList<Range> t = new ArrayList<>();
        int startX = -1;
        int opened = 0;
        for (Action act: actions) {
            if (act.t == 0) {
                if (opened == 0) {
                    startX = act.x;
                }
                opened++;
            } else {
                opened--;
                if (opened == 0) {
                    t.add(new Range(startX, act.x));
                }
            }
        }

        int c = n;
        int last = -1;
        for (Range r: t) {
            for (int i = last + 1; i < r.l; i++) {
                a[i] = c--;
            }
            for (int i = r.l; i <= r.r; i++) {
                a[i] = c;
            }
            last = r.r;
            c--;
        }
        for (int i = last + 1; i < n; i++) {
            a[i] = c--;
        }
        for (Range r: t2) {
            if (a[r.l] == a[r.r]) {
                write("NO\n");
                return;
            }
        }
        write("YES\n");
        for (int i = 0; i < n; i++) {
            write(a[i] + " ");
        }
        write("\n");
    }

    class Action implements Comparable<Action>{
        int t, x;
        Action(int t, int x) {
            this.t = t;
            this.x = x;
        }

        @Override
        public int compareTo(Action action) {
            if (x == action.x) {
                return Integer.compare(t, action.t);
            } else {
                return Integer.compare(x, action.x);
            }
        }
    }

    class Range {
        int l, r;
        Range(int l, int r) {
            this.l = l;
            this.r = r;
        }
    }








    public static void main(String[] args) throws FileNotFoundException, IOException {
        Main m = new Main();
        m.solve();
        try {
            m.out.close();
        } catch (IOException e) {}
    }

    BufferedReader in;
    BufferedWriter out;
    StringTokenizer tokenizer;
    public Main() {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new BufferedWriter(new OutputStreamWriter(System.out));
    }
    public String n() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(in.readLine());
            } catch (IOException e) {}
        }
        return tokenizer.nextToken();
    }
    public int ni() {
        return Integer.parseInt(n());
    }
    public long nl() {
        return Long.parseLong(n());
    }
    public void write(String s) {
        try {
            out.write(s);
        } catch (IOException e) {}
    }
}