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 powmod(long long base, long long exponent, long long mod) {
  long long result = 1;
  while (exponent > 0) {
    if (exponent % 2 == 0) {
      exponent /= 2;
      base = (base * base) % mod;
    } else {
      result = (result * base) % mod;
      exponent /= 2;
      base = (base * base) % mod;
    }
  }
  return result;
}
bool decresing(long long x, long long y) { return x > y; }
long long trin(long long start, long long stop) {
  return (stop - start + 1) * (stop + start) / 2;
}
bool sortvectorf(pair<long long, long long> a, pair<long long, long long> b) {
  return ((a.first > b.first) || (a.first == b.first && a.second > b.second));
}
bool sortvectors(pair<long long, long long> a, pair<long long, long long> b) {
  return ((a.second > b.second) || (a.second == b.second && a.first > b.first));
}
bool negasortvectorf(pair<long long, long long> a,
                     pair<long long, long long> b) {
  return ((a.first < b.first) || (a.first == b.first && a.second < b.second));
}
bool negasortvectors(pair<long long, long long> a,
                     pair<long long, long long> b) {
  return ((a.second < b.second) || (a.second == b.second && a.first < b.first));
}
vector<vector<long long>> findPermutations(vector<long long> &a) {
  sort(a.begin(), a.end());
  vector<vector<long long>> sol;
  do {
    sol.push_back(a);
  } while (next_permutation(a.begin(), a.end()));
  return sol;
}
long long gcd(long long a, long long b) {
  if (a == 0) {
    return b;
  }
  if (b == 0) {
    return a;
  }
  return gcd(b % a, a);
}
bool isprime(long long n) {
  for (int i = 2; i < n; i += 1) {
    if (i * i > n) {
      break;
    }
    if ((n / i) * i == n) {
      return false;
    }
  }
  return true;
}
long long fdivisor(long long n, long long fro) {
  for (int i = 1; i < n + 1; i += 1) {
    if ((n / i) * i == n && i >= fro) {
      return i;
    }
  }
  return -1;
}
vector<long long> divlist(long long n) {
  vector<long long> curr;
  for (int i = 2; i < n; i += 1) {
    if ((long long)i * i > n) {
      break;
    }
    if ((n / i) * i == n) {
      curr.push_back(i);
      curr.push_back(n / i);
    }
    if ((long long)i * i == n) {
      curr.pop_back();
    }
  }
  sort(curr.begin(), curr.end());
  return curr;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n;
  cin >> n;
  long long m;
  cin >> m;
  long long l = 0;
  vector<bool> sol(n);
  vector<pair<long long, long long>> q;
  sol[0] = true;
  for (int i = 0; i < m; i += 1) {
    long long a, b, c;
    cin >> a >> b >> c;
    if (a == 1) {
      for (int ii = b; ii < c; ii += 1) {
        sol[ii] = true;
      }
    } else {
      q.push_back({b, c});
      l++;
    }
  }
  for (int i = 0; i < l; i += 1) {
    bool good = false;
    for (int ii = q[i].first; ii < q[i].second; ii += 1) {
      if (sol[ii] == false) {
        good = true;
        break;
      }
    }
    if (!good) {
      cout << "NO" << endl;
      return 0;
    }
  }
  cout << "YES" << endl;
  long long curr = 5000;
  for (int i = 0; i < n; i += 1) {
    if (sol[i]) {
      curr += 2;
    }
    curr--;
    cout << curr << " ";
  }
  cout << endl;
  return 0;
}