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;
const int M = 1e5 + 10;
int n, m, to[M], c1, c0, ans[M];
struct d {
  int l, r;
  bool operator<(const d a) const { return r > a.r; }
} t1[M], t0[M];
int fnd(int x) {
  if (to[x] == x) return x;
  return to[x] = fnd(to[x]);
}
int main(int argc, char const *argv[]) {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) to[i] = i;
  for (int i = 1; i <= m; i++) {
    int t, l, r;
    scanf("%d%d%d", &t, &l, &r);
    if (t)
      t1[++c1].l = l, t1[c1].r = r;
    else
      t0[++c0].l = l, t0[c0].r = r;
  }
  sort(t1 + 1, t1 + 1 + c1);
  for (int i = 1; i <= c1; i++) {
    int l = t1[i].l, r = t1[i].r;
    for (int j = r - 1; j >= l; j--) to[j] = fnd(j + 1);
  }
  for (int i = n; i >= 1; i--)
    ans[i] = ans[i + 1] + (to[i] != to[i + 1] ? 1 : 0);
  for (int i = 1; i <= c0; i++) {
    int bad = 1, l = t0[i].l, r = t0[i].r;
    for (int j = l; j <= r - 1; j++)
      if (to[j] != to[j + 1]) {
        bad = 0;
        break;
      }
    if (bad) return 0 * printf("NO\n");
  }
  printf("YES\n");
  for (int i = 1; i <= n; i++) printf("%d ", ans[i]);
  return 0;
}