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 long long mod = 1e9 + 7;
const int maxn = 1e6 + 5;
const int INF = 0x7fffffff;
const long long inf = 0x3f3f3f3f;
const double eps = 1e-8;
void f() { return; }
int n, w;
int a[maxn];
pair<int, int> p1[maxn], p0[maxn];
int main() {
  f();
  int n, q;
  scanf("%d%d", &n, &q);
  a[0] = n + 1;
  for (int i = 1; i <= n; i++) a[i] = n - i + 1;
  int n1 = 0, n0 = 0;
  for (int j = 0; j < q; ++j) {
    int t;
    scanf("%d", &t);
    if (t == 0) {
      scanf("%d%d", &p0[n0].first, &p0[n0].second);
      n0++;
    } else {
      scanf("%d%d", &p1[n1].first, &p1[n1].second);
      n1++;
    }
  }
  sort(p1, p1 + n1);
  int pos = 0;
  for (int i = 1; i < n1; i++) {
    if (p1[pos].second >= p1[i].first) {
      p1[pos].second = max(p1[pos].second, p1[i].second);
    } else {
      p1[++pos] = p1[i];
    }
  }
  for (int i = 0; i <= pos; i++) {
    for (int j = p1[i].first; j <= p1[i].second; j++) {
      a[j] = a[p1[i].first];
    }
  }
  int flag = 1;
  for (int i = 0; i < n0; i++) {
    int f = 0;
    for (int j = p0[i].first + 1; j <= p0[i].second; j++) {
      if (a[j] != a[j - 1]) f = 1;
    }
    if (f == 0) flag = 0;
  }
  if (!flag)
    puts("NO");
  else {
    puts("YES");
    for (int i = 1; i <= n; i++) {
      printf("%d%c", a[i], i == n ? '\n' : ' ');
    }
  }
  return 0;
}