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;
const int N = 1004;
int n, m, a[N];
vector<pair<int, int> > V[2];
void sol() {
  sort(V[1].begin(), V[1].end());
  int val = (int)1e8;
  a[0] = val;
  for (pair<int, int> seg : V[1]) {
    int l = seg.first, r = seg.second;
    int set = -1;
    for (int i = l; i <= r; ++i) {
      if (a[i] != 0) set = a[i];
      assert(a[i] == 0 || set == a[i]);
    }
    if (set == -1) set = val - 1002;
    val -= 1002;
    for (int i = l; i <= r; ++i) a[i] = set;
  }
  for (int i = 1; i <= n; ++i)
    if (a[i] == 0) a[i] = a[i - 1] - 1;
  for (pair<int, int> seg : V[0]) {
    int l = seg.first, r = seg.second;
    bool ok = false;
    for (int i = l; i < r; ++i)
      if (a[i] > a[i + 1]) {
        ok = true;
        break;
      }
    if (!ok) {
      cout << "NO \n";
      exit(0);
    }
  }
  cout << "YES \n";
  for (int i = 1; i <= n; ++i) cout << a[i] << " ";
  cout << '\n';
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  if (fopen("input.txt", "r")) {
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
  }
  cin >> n >> m;
  cerr << "# " << n << " " << m << '\n';
  int t, l, r;
  for (int i = 1; i <= m; ++i) {
    cin >> t >> l >> r;
    V[t].push_back(pair<int, int>(l, r));
  }
  sol();
  return 0;
}