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 endzero = 9999, endone = -1, pmax, posline[1005][5], ansnum, pointer, n,
    res, m, a, b, c;
bool fail;
int fmax(int j) {
  while (posline[j][1] != 0) {
    j = posline[j][1];
  }
  return j;
}
int main() {
  cin >> n >> m;
  for (int i = 1; i <= m; i++) {
    cin >> a >> b >> c;
    if (a == 1) {
      posline[b][1] = max(posline[b][1], c);
    } else {
      if (posline[b][2] == 0)
        posline[b][2] = c;
      else
        posline[b][2] = min(posline[b][2], c);
    }
  }
  endone = -1;
  for (int i = 1; i <= n; i++) {
    if (endone <= 0 && posline[i][1] > 0) {
      endzero = 9999;
      endone = posline[i][1];
    } else
      endone = max(endone, posline[i][1]);
    if (posline[i][2] != 0) endzero = min(endzero, posline[i][2]);
    if (endzero <= endone) {
      fail = true;
      break;
    }
    if (endone == i) {
      endone = -1;
      endzero = 9999;
    }
  }
  if (fail)
    cout << "NO" << '\n';
  else {
    cout << "YES" << '\n';
    ansnum = 1000;
    pointer = 1;
    while (pointer <= n) {
      if (posline[pointer][1] > 0) {
        res = posline[pointer][1];
        while (pointer <= res && pointer <= n) {
          if (pointer == n)
            cout << ansnum << '\n';
          else
            cout << ansnum << ' ';
          res = max(res, posline[pointer][1]);
          ansnum++;
          pointer++;
        }
        ansnum -= 2;
      } else {
        if (pointer == n)
          cout << ansnum << '\n';
        else
          cout << ansnum << ' ';
        if (posline[pointer][2] != 0 && ansnum - 1 > 0) ansnum--;
        pointer++;
      }
    }
  }
}