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.*;

public class Main {
    public static void main(String[] args)
    {
        Scanner stdin = new Scanner(System.in);
        /*int n = stdin.nextInt();
        for(int i = 0; i < n; i++)
        {
        	test(stdin);
        }*/
        test(stdin);
        stdin.close();
    }
    public static void test(Scanner stdin)
    {
    	int n = stdin.nextInt();
    	int m = stdin.nextInt();
    	int[] dp = new int[n];
    	LinkedList<int[]> ns = new LinkedList<>();
    	for(int i = 0; i < m; i++)
    	{
    		int t = stdin.nextInt();
    		int l = stdin.nextInt() - 1;
    		int r = stdin.nextInt() - 1;
    		if(t == 1)
    		{
    			for(int u = l; u < r; u++)
    			{
    				dp[u] = t;
    			}
    		}
    		else
    		{
    			int[] a = {l,r};
    			ns.add(a);
    		}
    	}
    	for (int[] is : ns) {
			boolean np = true;
			for(int i = is[0]; i < is[1]; i++)
			{
				if(dp[i] < 1)
				{
					dp[i] = -1;
					np = false;
				}
			}
			if(np)
			{
				System.out.println("NO");
				return;
			}
		}
    	int cur = 20000;
    	System.out.println("YES");
    	StringBuilder b = new StringBuilder();
    	for(int i = 0; i < n; i++)
    	{
        	b.append(cur + " ");
        	cur += dp[i];
    	}
    	System.out.println(b);
    }
}