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 {

    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        int[] a = new int[n+1];
        Arrays.fill(a, 1);
        boolean[][] sorted = new boolean[n+2][n+2];
        PriorityQueue<int[]> q = new PriorityQueue<>(new Comparator<int[]>() {
            @Override
            public int compare(int[] t2, int[] t1) {
                if (t2[0] > t1[0]) {
                    return -1;
                } else {
                    return 1;
                }
            }
        });
        for (int i = 0; i < m; i++) {
            st = new StringTokenizer(in.readLine());
            int f = Integer.parseInt(st.nextToken());
            int l = Integer.parseInt(st.nextToken());
            int r = Integer.parseInt(st.nextToken());
            if (f == 1) {
                for (int j = l; j < r; j++) {
                    sorted[j][j + 1] = true;
                }
            } else {
                q.offer(new int[]{l, r});
            }
        }
        int cnt = 2;
        outer: while (!q.isEmpty()) {
            int[] f = q.poll();
            int l = f[0];
            int r = f[1];
            for (int j = l; j < r; j++) {
                if (!sorted[j][j+1]) {
                    a[j] = cnt;
                    cnt++;
                    continue outer;
                }
            }
            System.out.println("NO");
            return;
        }
        System.out.println("YES");
        for (int j = 1; j <= n; j++) {
            if (j > 1) {
                System.out.print(' ');
            }
            System.out.print(a[j]);
        }
        System.out.print('\n');
    }

}
/*
4 3
1 3 4
0 1 2
0 2 4


1 2 3 3
 */