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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {
    static BufferedReader br;
    static StringTokenizer st;

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

    static int nextInt() {
        return Integer.parseInt(nextToken());
    }


    static long nextLong() {
        return Long.parseLong(nextToken());
    }


    static double nextDouble() {
        return Double.parseDouble(nextToken());
    }


    static String next() {
        return nextToken();
    }


    static char nextChar() throws IOException {
        return (char) br.read();
    }

    static String nextLine() throws IOException {
        return br.readLine();
    }

    public static void main(String[] args) {
        br = new BufferedReader(new InputStreamReader(System.in));
        int n = nextInt();
        int m = nextInt();
        Pair[] pair = new Pair[m];
        for (int i = 0; i < m; i++) {
            pair[i] = new Pair(nextInt(), nextInt(), nextInt());
        }
        Arrays.sort(pair);
        boolean[] tr = new boolean[n - 1];
        int k = 0;
        for (int i = 0; i < m; i++) {
            if (pair[i].x == 0) {
                break;
            }
            for (int j = pair[i].y - 1; j < pair[i].z - 1; j++) {
                tr[j] = true;
            }
            k++;
        }
        for (int i = k; i < m; i++) {
            boolean tr2 = true;
            for (int j = pair[i].y - 1; j < pair[i].z - 1; j++) {
                if (!tr[j]) {
                    tr2 = false;
                    break;
                }
            }
            if (tr2) {
                System.out.println("NO");
                System.exit(0);
            }
        }
        System.out.println("YES");
        int[] ans = new int[n];
        ans[0] = 10000000;
        for (int i = 1; i < n; i++) {
            if (tr[i - 1]) {
                ans[i] = ans[i - 1];
            } else {
                ans[i] = ans[i - 1] - 1;
            }
        }
        for (int i = 0; i < ans.length; i++) {
            System.out.print(ans[i] + " ");
        }
    }

    static class Pair implements Comparable<Pair> {
        int x;
        int y;
        int z;

        public Pair(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        @Override
        public int compareTo(Pair o) {
            return Integer.compare(o.x, x);
        }
    }
}