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;
inline long long mod(long long n, long long m) {
  long long ret = n % m;
  if (ret < 0) ret += m;
  return ret;
}
long long gcd(long long a, long long b) { return (b == 0 ? a : gcd(b, a % b)); }
long long exp(long long a, long long b, long long m) {
  if (b == 0) return 1;
  if (b == 1) return mod(a, m);
  long long k = mod(exp(a, b / 2, m), m);
  if (b & 1) {
    return mod(a * mod(k * k, m), m);
  } else
    return mod(k * k, m);
}
long long pai[1111], n, m;
long long find(long long x) {
  return (x == pai[x]) ? x : pai[x] = find(pai[x]);
}
void join(long long a, long long b) {
  a = find(a);
  b = find(b);
  pai[a] = b;
}
signed main() {
  cin >> n >> m;
  vector<pair<long long, long long> > fora;
  for (long long i = 1; i <= n; i++) pai[i] = i;
  for (long long i = 0; i < m; i++) {
    long long t, l, r;
    cin >> t >> l >> r;
    if (t == 1) {
      for (long long j = l + 1; j <= r; j++) {
        join(l, j);
      }
    } else
      fora.push_back(pair<long long, long long>(l, r));
  }
  for (long long i = 0; i < (long long)fora.size(); i++) {
    if (find(fora[i].first) == find(fora[i].second)) {
      cout << "NO\n";
      return 0;
    }
  }
  long long ls = 1e6;
  long long a[n + 3];
  a[1] = ls;
  for (long long i = 2; i <= n; i++) {
    if (find(i - 1) != find(i)) ls--;
    a[i] = ls;
  }
  cout << "YES"
       << "\n";
  for (long long i = 1; i <= n; i++) cout << a[i] << " ";
  cout << "\n";
}