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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer sToken = new StringTokenizer(reader.readLine());
        int n = Integer.parseInt(sToken.nextToken());
        int m = Integer.parseInt(sToken.nextToken());
        int[] res = new int[n];
        int[][] given = new int[m][3];
        int[] right = new int[n];
        Arrays.fill(right, -1);
        for (int i=0; i<m; i++) {
            sToken = new StringTokenizer(reader.readLine());
            int t = Integer.parseInt(sToken.nextToken());
            int l = Integer.parseInt(sToken.nextToken()) - 1;
            int r = Integer.parseInt(sToken.nextToken()) - 1;
            given[i] = new int[]{t, l, r};
            if (t==1) right[l] = Math.max(right[l], r);
        }
        res[0] = n;
        int l = 0, r = right[0];
        for (int i=1; i<n; i++) {
            if (l<=i && i<=r) {
                r = Math.max(r, right[i]); res[i] = res[i-1];
            } else {
                l = i; r = right[i]; res[i] = res[i-1] - 1;
            }
        }
        for (int i=0; i<m; i++) {
            if (given[i][0]==0) {
                int L = given[i][1], R = given[i][2];
                boolean can = false;
                for (int j=L+1; j<=R; j++) {
                    if (res[j-1]>res[j]) {
                        can = true; break;
                    }
                }
                if (!can) {
                    System.out.println("NO"); return;
                }
            }
        }
        StringBuilder ans = new StringBuilder();
        ans.append("YES\n");
        for (int i=0; i<n; i++) ans.append(res[i]).append(" ");
        System.out.println(ans);
    }
}