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 long long N = 1e5 + 10;
long long n, m, a[N];
bool c[N];
struct query {
  long long t;
  long long l;
  long long r;
};
query q[N];
bool cmp(query x, query y) {
  if (x.t == y.t) {
    return x.l < y.l;
  }
  return x.t > y.t;
}
int main() {
  cin.tie(NULL);
  cout.tie(NULL);
  ios_base::sync_with_stdio(false);
  cin >> n >> m;
  long long p = 0;
  for (long long i = 1; i <= m; i++) {
    long long t, l, r;
    cin >> t >> l >> r;
    q[i].t = t;
    q[i].l = l;
    q[i].r = r;
    if (t == 1) {
      p++;
    }
  }
  sort(q + 1, q + m + 1, cmp);
  for (long long i = 1; i <= n; i++) {
    c[i] = false;
    a[i] = n;
  }
  for (long long i = 1; i <= p; i++) {
    long long l = q[i].l;
    long long r = q[i].r;
    for (long long j = l + 1; j <= r; j++) {
      c[j] = true;
    }
  }
  bool mcheck = true;
  for (long long i = p + 1; i <= m; i++) {
    long long l = q[i].l;
    long long r = q[i].r;
    bool check = false;
    for (long long i = l; i <= r - 1; i++) {
      if (a[i] > a[i + 1]) {
        check = true;
        break;
      }
    }
    if (check) {
      continue;
    }
    check = false;
    for (long long i = l + 1; i <= r; i++) {
      if (a[i] >= a[i - 1] && !c[i]) {
        a[i] = a[i - 1] - 1;
        check = true;
        break;
      }
    }
    if (!check) {
      mcheck = false;
      break;
    }
  }
  if (mcheck) {
    cout << "YES\n";
    for (long long i = 1; i <= n; i++) {
      cout << a[i] << " ";
    }
  } else {
    cout << "NO\n";
  }
}