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 A[300010], B[300010];
struct Q {
  int l, r, k;
} a[1010];
int cmp(Q b, Q c) {
  if (b.l == c.l) return b.r < c.r;
  return b.l < c.l;
}
int main() {
  int i, n, j, m, x;
  scanf("%d%d", &n, &m);
  for (i = 1; i <= m; i++) scanf("%d%d%d", &a[i].k, &a[i].l, &a[i].r);
  sort(a + 1, a + 1 + m, cmp);
  for (i = 1; i <= m; i++) {
    if (a[i].k) {
      if (A[a[i].l] == 0)
        x = (m - i + 1) * 10000;
      else
        x = A[a[i].l];
      for (j = a[i].l; j <= a[i].r; j++) A[j] = x;
    }
  }
  for (i = 1; i <= m; i++) {
    if (a[i].k == 0) {
      if (A[a[i].l] == A[a[i].r] && A[a[i].l]) {
        cout << "NO" << endl;
        return 0;
      }
    }
  }
  cout << "YES" << endl;
  A[0] = 1e9;
  for (i = 1; i <= n; i++) {
    if (A[i] == 0) A[i] = A[i - 1] - 1;
    cout << A[i] << " ";
  }
  return 0;
}