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 maxn = 1e3 + 13;
int n, m, f, l, r, a[maxn];
struct edge {
  int L, R;
} s[maxn], t[maxn];
bool cmp(edge a, edge b) { return a.L < b.L; }
int main() {
  cin >> n >> m;
  int nums = 0, numt = 0;
  while (m--) {
    cin >> f >> l >> r;
    if (f) {
      s[nums].L = l;
      s[nums].R = r;
      nums++;
    } else {
      t[numt].L = l;
      t[numt].R = r;
      numt++;
    }
  }
  sort(s, s + nums, cmp);
  int val = 1e8, rr = 0;
  for (int i = 0; i < nums; ++i) {
    if (s[i].L > rr) {
      rr = s[i].R;
      val -= 2000;
      for (int j = s[i].L; j <= s[i].R; ++j) a[j] = val;
    } else {
      for (int j = s[i].L; j <= s[i].R; ++j) a[j] = val;
      rr = max(rr, s[i].R);
    }
  }
  a[0] = 2e8;
  for (int i = 1; i <= n; ++i) {
    if (!a[i]) a[i] = a[i - 1] - 1;
  }
  bool flag = true;
  for (int i = 0; i < numt; ++i) {
    if (a[t[i].L] == a[t[i].R]) flag = false;
  }
  if (flag) {
    puts("YES");
    for (int i = 1; i <= n; ++i) cout << a[i] << " ";
  } else
    puts("NO");
  return 0;
}