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.util.Scanner;

public class ProblemC {
    
    static int t[] = new int[1005];
    static int l[] = new int[1005];
    static int r[] = new int[1005];
    static int a[] = new int[1005];
    static int s[] = new int[1005];

    public static void main(String[] args) {
        for (int i = 0; i < 1005; i ++) s[i] = 0;
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        for (int i = 1; i <= m; i ++) {
            t[i] = scanner.nextInt();
            l[i] = scanner.nextInt();
            r[i] = scanner.nextInt();
            for (int j = l[i] + 1; j <= r[i]; j ++) {
                s[j] |= (t[i] + 1);
            }
        }
        a[1] = 5000;
        for (int i = 2; i <= n; i ++) {
            //System.out.println(s[i]);
            if ((s[i] & 2) != 0) {
                a[i] = a[i - 1];
            } else if ((s[i] & 1) != 0) {
                a[i] = a[i - 1] - 1;
            } else {
                a[i] = a[i - 1];
            }
        }
        boolean ok = true;
        for (int i = 1; i <= m; i ++) {
            if (t[i] == 1) {
                for (int j = l[i] + 1; j <= r[i]; j ++) {
                    if (a[j-1] > a[j]) {
                        ok = false;
                        break;
                    }
                }
            } else if (t[i] == 0) {
                boolean ok2 = false;
                for (int j = l[i] + 1; j <= r[i]; j ++) {
                    if (a[j-1] > a[j]) {
                        ok2 = true;
                        break;
                    }
                }
                if (ok2 == false) {
                    ok = false;
                    break;
                }
            }
            if (ok == false) break;
        }
        if (ok == false) {
            System.out.println("NO");
        } else {
            System.out.println("YES");
            for (int i = 1; i <= n; i ++) {
                System.out.print(a[i]);
                System.out.print(" ");
            }
            System.out.println();
        }
        scanner.close();
    }
    
}