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.BufferedWriter;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Scanner;

public class VasyaAndArray {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = in.nextInt();
        int m = in.nextInt();
        int[][] facts = new int[m][3];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < 3; j++) {
                facts[i][j] = in.nextInt();
            }
        }
        int[] array = new int[n + 1];
        array[0] = 0;
        for (int i = 1; i <= n; i++) {
            boolean mustBeSorted = false;
            for (int[] fact : facts) {
                if (fact[0] == 1 && fact[1] <= i - 1 && fact[2] >= i) {
                    mustBeSorted = true;
                    break;
                }
            }
            if (mustBeSorted) {
                array[i] = array[i - 1];
            } else {
                array[i] = array[i - 1] - 1;
            }
        }
        boolean valid = true;
        for (int[] fact : facts) {
            if (fact[0] == 0) {
                boolean isSorted = true;
                for (int i = fact[1] + 1; i <= fact[2]; i++) {
                    if (array[i] < array[i - 1]) {
                        isSorted = false;
                        break;
                    }
                }
                if (isSorted) {
                    valid = false;
                    break;
                }
            }
        }
        if (valid) {
            out.println("YES");
            for (int i = 1; i < n; i++) {
                array[i] += 1 - array[n];
                out.print(array[i] + " ");
            }
            array[n] += 1 - array[n];
            out.println(array[n]);
        } else {
            out.println("NO");
        }
        out.flush();
    }
}