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 cre {
  int l, r;
  cre(int _l, int _r) : l(_l), r(_r) {}
  bool operator<(const cre& o) const { return l < o.l; }
};
vector<cre> seg[2], a;
int n, m;
int ans[1005];
int main() {
  ios::sync_with_stdio(false);
  cin >> n >> m;
  int id, x, y;
  for (int i = 1; i <= m; i++) {
    cin >> id >> x >> y;
    seg[id].push_back(cre(x, y));
  }
  if (seg[1].empty()) {
    cout << "YES" << endl;
    for (int i = n; i >= 1; i--) {
      cout << i << " ";
    }
    cout << endl;
    return 0;
  }
  sort(seg[1].begin(), seg[1].end());
  int nowl = 0, nowr = 0;
  for (auto& it : seg[1]) {
    if (nowr < it.l) {
      if (nowr > 0) a.push_back(cre(nowl, nowr));
      nowl = it.l;
      nowr = it.r;
    } else {
      nowr = max(it.r, nowr);
    }
  }
  a.push_back(cre(nowl, nowr));
  int now = 10000000;
  ans[1] = now;
  int pre = 0;
  for (auto& it : a) {
    for (int i = pre + 1; i <= it.l; i++) {
      ans[i] = --now;
    }
    for (int i = it.l + 1; i <= it.r; i++) {
      ans[i] = now;
    }
    pre = it.r;
  }
  if (pre < n) {
    for (int i = pre + 1; i <= n; i++) {
      ans[i] = --now;
    }
  }
  for (auto& it : seg[0]) {
    bool flag = 0;
    for (int i = it.l; i < it.r; i++) {
      if (ans[i] > ans[i + 1]) {
        flag = 1;
        break;
      }
    }
    if (flag == 0) {
      cout << "NO" << endl;
      return 0;
    }
  }
  cout << "YES" << endl;
  for (int i = 1; i <= n; i++) {
    cout << ans[i] << " ";
  }
  cout << endl;
}