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;
template <int D, typename T>
struct Vec : public vector<Vec<D - 1, T>> {
  static_assert(D >= 1, "Vector dimension must be greater than zero!");
  template <typename... Args>
  Vec(int n = 0, Args... args)
      : vector<Vec<D - 1, T>>(n, Vec<D - 1, T>(args...)) {}
};
template <typename T>
struct Vec<1, T> : public vector<T> {
  Vec(int n = 0, const T& val = T()) : vector<T>(n, val) {}
};
long long int power(long long int x, long long int y, long long int p) {
  long long int res = 1;
  x = x % p;
  if (y == 0) return 1;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
int gcd(int a, int b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long int modinv(long long int a, long long int p) {
  return power(a, p - 2, p);
}
void solve() {
  long long int n, m;
  cin >> n >> m;
  std::set<pair<long long int, long long int>> v, s;
  for (long long int i = 0; i < m; i++) {
    long long int t, l, m;
    cin >> t >> l >> m;
    if (t == 1) {
      v.insert(make_pair(l - 1, m - 1));
    } else {
      s.insert(make_pair(l - 1, m - 1));
    }
  }
  Vec<1, long long int> arr(n, 0);
  long long int val = 1000;
  for (auto p : v) {
    long long int a = p.first;
    long long int b = p.second;
    val = 1000 - a;
    if (arr[a] != 0) {
      val = arr[a];
    }
    for (long long int i = a; i <= b; i += 1) {
      arr[i] = val;
    }
  }
  for (long long int i = 0; i < n; i++) {
    if (arr[i] == 0) {
      arr[i] = 1000 - i;
    }
  }
  bool exists = true;
  for (auto p : s) {
    long long int a = p.first;
    long long int b = p.second;
    if (arr[a] == arr[b]) {
      exists = false;
    }
  }
  if (exists) {
    cout << "yes" << endl;
    for (auto p : arr) {
      cout << p << " ";
    }
  } else
    cout << "no" << endl;
  return;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int T = 1;
  for (long long int c = 0; c < T; c++) {
    solve();
  }
  return 0;
}