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;
int main() {
  int n, m;
  cin >> n >> m;
  vector<pair<int, int>> sorted;
  vector<pair<int, int>> unsorted;
  for (int i = 0; i < (m); i++) {
    int type, left, right;
    cin >> type >> left >> right;
    if (type == 1) {
      sorted.push_back(pair<int, int>(left, right));
    } else {
      unsorted.push_back(pair<int, int>(left, right));
    }
  }
  sort(sorted.begin(), sorted.end(),
       [](const pair<int, int> a, const pair<int, int> b) {
         return a.first < b.first;
       });
  vector<pair<int, int>> sortedReverse;
  int lastPointSorted = 1;
  for (pair<int, int> p : sorted) {
    if (p.first <= lastPointSorted) {
      if (p.second > lastPointSorted) {
        lastPointSorted = p.second;
      }
    } else {
      sortedReverse.push_back(pair<int, int>(lastPointSorted, p.first));
      lastPointSorted = p.second;
    }
  }
  if (lastPointSorted != n) {
    sortedReverse.push_back(pair<int, int>(lastPointSorted, n));
  }
  bool isNormal = true;
  if (!unsorted.empty() && sortedReverse.empty()) {
    isNormal = false;
  } else {
    for (pair<int, int> p : unsorted) {
      bool isPairNormal = false;
      for (pair<int, int> pr : sortedReverse) {
        if (!(pr.first <= p.first && pr.second <= p.first ||
              pr.first >= p.second && pr.second >= p.second)) {
          isPairNormal = true;
          break;
        }
      }
      if (!isPairNormal) {
        isNormal = false;
        break;
      }
    }
  }
  if (isNormal) {
    cout << "YES" << endl;
    int currNum = 1000;
    vector<pair<int, int>>::iterator it = sortedReverse.begin();
    for (int i = 1; i <= n; i++) {
      cout << currNum << " ";
      if (it != sortedReverse.end()) {
        if (i < it->first) {
          currNum++;
        } else if (i < it->second) {
          currNum--;
        } else {
          it++;
          currNum++;
        }
      } else {
        currNum++;
      }
    }
  } else {
    cout << "NO" << endl;
  }
}