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 C {
    class pair implements Comparable<pair> {
        int p;
        int t;

        public pair(int p, int t) {
            this.p = p;
            this.t = t;
        }

        @Override
        public int compareTo(pair o) {
            if (p == o.p) {
                return t - o.t;
            }
            return p - o.p;
        }
    }

    public void solve() throws IOException {
        int n = nextInt();
        int m = nextInt();
        int[] a = new int[n];
        ArrayList<pair> ones = new ArrayList<pair>();
        Set<pair> zers = new HashSet<>();
        for (int i = 0; i < m; ++i) {
            int t = nextInt();
            int l = nextInt() - 1;
            int r = nextInt() - 1;
            if (t == 0) {
                zers.add(new pair(l, r));
            } else {
                ones.add(new pair(l, -1));
                ones.add(new pair(r, 1));
            }
        }
        Collections.sort(ones);
        int counter = 0;
        int ind = 0;
        int color = 1;
        int i = 0;
        while (i < n && ind < ones.size()) {
            while (ind < ones.size() && ones.get(ind).p == i) {
                if (ones.get(ind).t == -1) {
                    ++counter;
                    a[i] = color;
                    ++ind;
                } else {
                    a[i] = color;
                    --counter;
                    ++ind;
                    if (counter == 0) ++color;
                }
            }
            {
                if (counter > 0) {
                    a[i] = color;
                }
            }
            ++i;
        }
        for (pair x : zers) {
            if (a[x.p] != 0 && a[x.p] == a[x.t]) {
                out.println("NO");
                return;
            }
        }
        out.println("YES");
        ind = 0;
        if (a[0] == 0) {
            a[0] = 100000;
            ind = 1;
        } else {
            a[0] = 1007 - a[0];
        }

        for (i = 1; i < n; ++i) {
            if (a[i] > 0) {
                a[i] = 1007 - a[i] - ind;
            } else {
                a[i] = a[i - 1] - 1;
                ++ind;
            }
        }
        for (i = 0; i < n; ++i) {
            out.print(a[i] + " ");
        }
    }

    public void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    BufferedReader br;
    StringTokenizer in;
    PrintWriter out;

    public String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public int[] nextArr(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = nextInt();
        }
        return res;
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        new C().run();
    }
}