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;
struct mar {
  int l;
  int r;
} w[10000];
int n, m, t, l, r, a = 1, i, j, v[10000], b = 1, x[10000], ok = 1, s;
int main() {
  cin >> n >> m;
  for (i = 1; i <= m; i++) {
    cin >> t >> l >> r;
    if (t == 1) {
      if (v[l] != 0) {
        if (v[r] == 0)
          for (j = l; j <= r; j++) v[j] = v[l];
        else if (v[r] != 0) {
          s = v[r];
          j = r + 1;
          while (v[j] == s) {
            v[j] = v[l];
            j++;
          }
          for (j = l; j <= r; j++) v[j] = v[l];
        }
        a++;
      } else if (v[l] == 0) {
        if (v[r] == 0)
          for (j = l; j <= r; j++) v[j] = a;
        else if (v[r] != 0) {
          s = v[r];
          j = r + 1;
          while (v[j] == s) {
            v[j] = a;
            j++;
          }
          for (j = l; j <= r; j++) v[j] = a;
        }
        a++;
      }
    } else {
      w[b].l = l;
      w[b].r = r;
      b++;
    }
  }
  int y = n - 1;
  x[1] = n;
  for (i = 2; i <= n; i++) {
    if (v[i] == v[i - 1] && v[i] != 0)
      x[i] = x[i - 1];
    else {
      x[i] = y;
      y--;
    }
  }
  b--;
  while (b) {
    if (x[w[b].r] < x[w[b].l]) {
      b--;
    } else {
      b = 0;
      ok = 0;
    }
  }
  if (ok == 1) {
    cout << "YES" << endl;
    for (int i = 1; i <= n; i++) cout << x[i] << " ";
  } else
    cout << "NO" << endl;
  return 0;
}