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;
vector<pair<int, int> > inc, deck;
int a[1000 + 50];
bool deccc[1000 + 50];
int sizz[1000 + 50];
int par[1000 + 50];
int root(int x) {
  while (par[x] != x) {
    par[x] = par[par[x]];
    x = par[x];
  }
  return x;
}
void uni(int x, int y) {
  if (x == y) {
    return;
  }
  x = root(x);
  y = root(y);
  if (sizz[x] < sizz[y]) {
    sizz[y] += sizz[x];
    par[x] = y;
  } else {
    sizz[x] += sizz[y];
    par[y] = x;
  }
}
int main() {
  int n, m, t, x, y;
  int maxx = 5000001;
  cin >> n >> m;
  for (int i = 1; i <= n; i++) {
    par[i] = i;
    sizz[i] = 1;
  }
  for (int i = 0; i < m; i++) {
    cin >> t >> x >> y;
    if (t == 1) {
      inc.push_back(make_pair(x, y));
    } else {
      deck.push_back(make_pair(x, y));
    }
  }
  sort(inc.begin(), inc.end());
  int le = -1;
  for (auto bcc : inc) {
    for (int i = bcc.first; i <= bcc.second; i++) {
      uni(bcc.first, i);
    }
  }
  int minn = maxx - 1;
  sort(deck.begin(), deck.end());
  bool poss = true;
  for (auto bcc : deck) {
    if (root(bcc.first) == root(bcc.second)) {
      poss = false;
      cout << "NO";
      return 0;
    }
  }
  int pre = -1;
  long long res = 999999;
  cout << "YES\n";
  for (int i = 1; i <= n; i++) {
    if (root(i) != pre) {
      pre = root(i);
      res--;
    }
    cout << res << " ";
  }
  return 0;
}