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>
int main() {
  int n, m;
  std::cin >> n >> m;
  std::pair<int, int> sorted[1010];
  int cntSorted = 0;
  std::pair<int, int> nSorted[1010];
  int ncntSorted = 0;
  for (int i = 0; i < m; ++i) {
    int t;
    std::cin >> t;
    if (t == 1) {
      std::cin >> sorted[cntSorted].first >> sorted[cntSorted].second;
      --sorted[cntSorted].first;
      --sorted[cntSorted].second;
      ++cntSorted;
    } else {
      std::cin >> nSorted[ncntSorted].first >> nSorted[ncntSorted].second;
      --nSorted[ncntSorted].first;
      --nSorted[ncntSorted].second;
      ++ncntSorted;
    }
  }
  std::sort(sorted, sorted + cntSorted);
  std::sort(nSorted, nSorted + ncntSorted);
  int ans[1010] = {0};
  int curCnt = 1e8;
  for (int i = 0; i < cntSorted; ++i) {
    int l = sorted[i].first, r = sorted[i].second;
    if (ans[l] == 0) {
      curCnt -= 1010;
    }
    for (int j = l; j <= r; ++j) ans[j] = curCnt;
  }
  int cur = 1e8 + 1e5;
  for (int i = 0; i < n; ++i) {
    if (ans[i] == 0)
      ans[i] = cur, --cur;
    else
      cur = ans[i] - 1;
  }
  for (int i = 0; i < ncntSorted; ++i) {
    int l = nSorted[i].first, r = nSorted[i].second;
    bool flag = false;
    for (int j = l + 1; j <= r; ++j) {
      if (ans[j] < ans[j - 1]) flag = true;
    }
    if (!flag) {
      std::cout << "NO";
      return 0;
    }
  }
  std::cout << "YES\n";
  for (int i = 0; i < n; ++i) std::cout << ans[i] << " ";
}