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;
long long power(long long x, long long y);
long long mpower(long long x, long long y, long long p);
long long modInv(long long a, long long m);
long long gcdExtended(long long a, long long b, long long *x, long long *y);
bool isPrime(long long n);
bool myf(pair<long long, long long> a, pair<long long, long long> b) {
  if (a.first == b.first) {
    return a.second < b.second;
  }
  return a.first < b.first;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t, i, j, k, l, h, p, q, r, x, y, z, a, b, c, d, f, n, m,
      M = 1000000007;
  char ch, ch2, ch3;
  string s, s1, s2, s3;
  vector<pair<long long, long long> > v, w;
  vector<long long>::iterator itrv;
  map<long long, long long> N;
  set<long long> S;
  set<long long>::iterator itr;
  cin >> n >> m;
  long long A[n];
  for (i = 0; i < n; i++) {
    A[i] = LLONG_MAX;
  }
  long long B[m][3];
  for (i = 0; i < m; i++) {
    for (j = 0; j < 3; j++) {
      cin >> B[i][j];
    }
    if (B[i][0]) {
      for (j = B[i][1]; j < B[i][2]; j++) {
        A[j] = 0;
      }
    }
  }
  for (i = 0; i < m; i++) {
    if (!B[i][0]) {
      v.push_back(make_pair(B[i][1], B[i][2]));
    }
  }
  sort(v.begin(), v.end(), myf);
  f = 0;
  for (i = 0; i < v.size(); i++) {
    long long first = 0;
    x = v[i].first;
    y = v[i].second;
    for (j = x; j < y; j++) {
      if (A[j] < 0) {
        first = 1;
        break;
      }
      if (A[j] == LLONG_MAX) {
        A[j] = -1;
        first = 1;
        break;
      }
    }
    if (!first) {
      f = 1;
      break;
    }
  }
  for (i = 0; i < n; i++) {
    if (A[i] == LLONG_MAX) {
      A[i] = 0;
    }
  }
  if (f) {
    cout << "NO" << endl;
    return 0;
  }
  cout << "YES\n";
  A[0] = 1e9;
  for (i = 1; i < n; i++) {
    A[i] += A[i - 1];
  }
  for (i = 0; i < n; i++) {
    cout << A[i] << " ";
  }
  return 0;
}
long long modInv(long long a, long long m) {
  long long x, y;
  long long g = gcdExtended(a, m, &x, &y);
  long long res = (x % m + m) % m;
  return res;
}
long long gcdExtended(long long a, long long b, long long *x, long long *y) {
  if (a == 0) {
    *x = 0, *y = 1;
    return b;
  }
  long long x1, y1;
  long long gcd = gcdExtended(b % a, a, &x1, &y1);
  *x = y1 - (b / a) * x1;
  *y = x1;
  return gcd;
}
long long mpower(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long power(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = res * x;
    y = y >> 1;
    x = x * x;
  }
  return res;
}
bool isPrime(long long n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  long long p = sqrt(n);
  for (int i = 5; i <= p; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}