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 = 1000000007ll;
long long powmod(long long a, long long b) {
  long long res = 1;
  a %= MOD;
  assert(b >= 0);
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % MOD;
    a = a * a % MOD;
  }
  return res;
}
template <typename t1, typename t2>
inline bool upmax(t1 &a, t2 b) {
  if (a < (t1)b) {
    a = (t1)b;
    return true;
  } else
    return false;
}
template <typename t1, typename t2>
inline bool upmin(t1 &a, t2 b) {
  if (a > (t1)b) {
    a = (t1)b;
    return true;
  } else
    return false;
}
template <typename T>
inline T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <typename T>
inline T lcm(T a, T b) {
  return a * (b / gcd(a, b));
}
template <typename T>
inline T sqr(T a) {
  return a * a;
}
int dx[] = {1, 0, -1, 0, 1, 1, -1, -1};
int dy[] = {0, 1, 0, -1, 1, -1, 1, -1};
int dkx[] = {-1, -1, 1, 1, -2, -2, 2, 2};
int dky[] = {-2, 2, -2, 2, -1, 1, -1, 1};
const int INF = 1000000404;
const long long LINF = 1e18 * (1ll);
const long double PI = 3.14159265358979323846;
const long double EPS = 1e-9;
const int SQ = 318;
int timer = 0;
vector<pair<int, int> > asc;
vector<pair<int, int> > none;
int a[1010];
void solve() {
  int n;
  cin >> n;
  int m;
  cin >> m;
  for (int(i) = (1); (i) < (n + 1); (i)++) a[i] = n - i + 1;
  for (int(i) = (0); (i) < (m); (i)++) {
    int f;
    int l, r;
    cin >> f >> l >> r;
    if (f) {
      asc.push_back(make_pair(l, r));
    } else
      none.push_back(make_pair(l, r));
  }
  sort((asc).begin(), (asc).end());
  sort((none).begin(), (none).end());
  vector<pair<int, int> > full_asc;
  int last = 0;
  int s, t;
  t = 0;
  int now = 1e6;
  for (auto [l, r] : asc) {
    if (l > t) {
      if (t != 0) {
        for (int(i) = (s); (i) < (t + 1); (i)++) {
          a[i] = now;
        }
        now--;
      }
      if (t + 1 < l) {
        for (int(i) = (t + 1); (i) < (l); (i)++) {
          a[i] = now--;
        }
      }
      s = l;
      t = r;
    } else {
      upmax(t, r);
    }
  }
  if (t != 0) {
    for (int(i) = (s); (i) < (t + 1); (i)++) {
      a[i] = now;
    }
    now--;
  }
  for (auto [l, r] : none) {
    if (a[l] == a[r]) {
      cout << "NO";
      return;
    }
  }
  cout << "YES" << endl;
  for (int(i) = (1); (i) < (n + 1); (i)++) {
    cout << a[i] << ' ';
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  for (int i = 1; i <= t; i++) {
    solve();
  }
  return 0;
}