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;
inline void read(int &res) {
  register int g = 1;
  register char ch = getchar();
  res = 0;
  while (!isdigit(ch)) {
    if (ch == '-') g = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    res = (res << 3) + (res << 1) + (ch ^ 48);
    ch = getchar();
  }
  res *= g;
}
struct P {
  int t, l, r;
  friend bool operator<(P a, P b) { return a.t > b.t; }
} p[1010];
int n, m, a[1010], sn;
int main() {
  read(n);
  read(m);
  for (register int i = 1; i <= m; i++) {
    read(p[i].t);
    read(p[i].l);
    read(p[i].r);
  }
  sort(p + 1, p + 1 + m);
  memset(a, 0, sizeof(a));
  for (register int i = 1; i <= m; i++) {
    if (p[i].t) {
      p[i].r = min(p[i].r, n);
      for (register int j = p[i].l; j <= p[i].r - 1; j++) {
        a[j] = 1;
      }
    } else {
      sn = 1;
      if (p[i].l == p[i].r) continue;
      p[i].r = min(p[i].r, n);
      for (register int j = p[i].l; j <= p[i].r - 1; j++) {
        if (a[j] != 1) {
          a[j] = -1;
          sn = 0;
          break;
        }
      }
      if (sn) break;
    }
  }
  if (sn) {
    printf("NO");
    return 0;
  }
  printf("YES\n");
  sn = 10000;
  for (register int i = 1; i <= n; i++) {
    printf("%d ", sn);
    sn += a[i];
  }
  return 0;
}