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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int a, b, c, i, j, k, p, l, m, n;
  long long int l1, l2, r1, r2;
  cin >> a >> b;
  long long int info[b][3];
  bool check = true;
  for (i = 0; i < b; i++) {
    cin >> info[i][0] >> info[i][1] >> info[i][2];
  }
  long long int verify[a];
  for (i = 0; i < a; i++) verify[i] = false;
  for (i = 0; i < b; i++) {
    if (info[i][0] == 1) {
      for (j = 0; j < b; j++) {
        if (info[j][0] == 1 && j != i) {
          l1 = info[i][1];
          r1 = info[i][2];
          l2 = info[j][1];
          r2 = info[j][2];
          if (l1 < l2 && r1 >= l2 && r1 <= r2) {
            info[j][1] = l1;
            info[i][2] = r2;
          } else if (l1 >= l2 && l1 <= r2 && r1 <= r2) {
            info[i][1] = l2;
            info[i][2] = r2;
          }
        }
      }
    }
  }
  for (i = 0; i < b; i++) {
    if (info[i][0] == 0) {
      for (j = 0; j < b; j++) {
        if (info[j][0] == 1) {
          l1 = info[i][1];
          r1 = info[i][2];
          l2 = info[j][1];
          r2 = info[j][2];
          if (l1 >= l2 && r1 <= r2) {
            check = false;
            break;
          }
        }
      }
    }
  }
  if (!check) {
    cout << "NO"
         << "\n";
  } else {
    cout << "YES" << '\n';
    long long int final[a];
    for (i = 0; i < b; i++) {
      if (info[i][0] == 1) {
        k = a - info[i][1] + 1;
        for (j = info[i][1] - 1; j < info[i][2]; j++) {
          verify[j] = k;
          final[j] = k;
        }
      }
    }
    long long int count = 0;
    j = a;
    for (i = 0; i < a; i++, j--) {
      if (verify[i] == 0) {
        final[i] = j;
        count++;
      }
      cout << final[i] << ' ';
    }
    cout << '\n';
  }
}