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 issorted[1003];
int ans[1003];
int parent[1003];
void init() {
  for (int i = 0; i < 1003; i++) {
    parent[i] = i;
  }
}
int getParent(int x) {
  if (x == parent[x]) return x;
  return parent[x] = getParent(parent[x]);
}
void join(int x, int y) {
  x = getParent(x);
  y = getParent(y);
  if (x != y) {
    parent[y] = x;
  }
}
struct state {
  int t, l, r;
  state() {}
  state(int t, int l, int r) : t(t), l(l), r(r) {}
  bool operator<(const state o) const {
    if (t != o.t) return t > o.t;
    if (l != o.l) return l < o.l;
    return r < o.r;
  }
};
int main() {
  int n, m;
  cin >> n >> m;
  vector<state> vec;
  init();
  for (int i = 0; i < m; i++) {
    int t, l, r;
    cin >> t >> l >> r;
    vec.push_back(state(t, l, r));
  }
  sort(vec.begin(), vec.end());
  int sort_id = 1;
  for (auto st : vec) {
    int t = st.t;
    int l = st.l;
    int r = st.r;
    if (t) {
      for (int i = l; i <= r; i++) {
        issorted[i] = true;
        join(l, i);
      }
    } else {
      bool issorted_range = true;
      for (int i = l; i <= r; i++) issorted_range |= issorted[i];
      if (issorted_range && getParent(l) == getParent(r)) {
        return cout << "NO\n", 0;
      }
    }
  }
  int num = 1;
  int last_id = 0;
  for (int i = n; i >= 1; i--) {
    if (issorted[i]) {
      if (getParent(i) != last_id) {
        num++;
        last_id = getParent(i);
      }
      ans[i] = num;
    } else {
      ans[i] = ++num;
    }
  }
  cout << "YES\n";
  for (int i = 1; i <= n; i++) cout << ans[i] << " ";
  return 0;
}