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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author Andy Phan
 */
public class c {
    static int MAX = 1000000000;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        boolean[] forbid = new boolean[n];
        ArrayList<Range> bs = new ArrayList<>();
        for(int i = 0; i < m; i++) {
            if(in.nextInt() == 1) {
                int l = in.nextInt()-1;
                int r = in.nextInt()-1;
                for(int j = l+1; j <= r; j++) forbid[j] = true;
            } else {
                bs.add(new Range(in.nextInt()-1, in.nextInt()-1));
            }
        }
        
        boolean[] neg = new boolean[n];
        for(Range r : bs) {
            boolean found = false;
            for(int i = r.l+1; i <= r.r; i++) {
                if(!forbid[i]) {
                    neg[i] = true;
                    found = true;
                    break;
                }
            }
            if(found) continue;
            System.out.println("NO");
            return;
        }
        System.out.println("YES");
        int curr = MAX;
        for(int i = 0; i < n; i++) {
            if(neg[i]) curr--;
            System.out.print(curr + " ");
        }
        System.out.println();
    }
    
    static class Range {
        int l, r;
        
        public Range(int le, int ri) {
            l = le;
            r = ri;
        }
    }
}