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;
int xx[4] = {1, -1, 0, 0};
int yy[4] = {0, 0, 1, -1};
const double eps = 1e-9;
const int maxn = 2e6 + 5000;
const long long mod = 1e9 + 7;
const int INF(0x3f3f3f3f);
const long long INFL(0x3f3f3f3f3f3f3f3fll);
inline int sign(double a) { return a < -eps ? -1 : a > eps; }
long long mul(long long a, long long b, long long c) {
  long long res = 1;
  while (b) {
    if (b & 1) res *= a, res %= c;
    a *= a, a %= c, b >>= 1;
  }
  return res;
}
long long phi(long long x) {
  long long res = x;
  for (long long i = 2; i * i <= x; i++) {
    if (x % i == 0) res = res / i * (i - 1);
    while (x % i == 0) x /= i;
  }
  if (x > 1) res = res / x * (x - 1);
  return res;
}
template <typename A, typename B>
inline bool chmin(A& a, B b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename A, typename B>
inline bool chmax(A& a, B b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename A, typename B>
inline long long add(A x, B y) {
  if (x + y < 0) return x + y + mod;
  return x + y >= mod ? x + y - mod : x + y;
}
template <typename A, typename B>
inline void add2(A& x, B y) {
  if (x + y < 0)
    x = x + y + mod;
  else
    x = (x + y >= mod ? x + y - mod : x + y);
}
template <typename A, typename B>
inline long long mul1(A x, B y) {
  return 1ll * x * y % mod;
}
template <typename A, typename B>
inline void mul2(A& x, B y) {
  x = (1ll * x * y % mod + mod) % mod;
}
template <typename A>
inline void debug(A a) {
  cout << a << '\n';
}
template <typename A>
inline long long sqr(A x) {
  return 1ll * x * x;
}
template <typename A>
A inv(A x) {
  return mul(x, mod - 2);
}
template <typename A>
void bugl(A a[], int l, int r) {
  for (int i = l; i <= r; i++) cout << a[i] << " ";
  cout << endl;
}
template <typename A>
void bug(A a[], int l, int r) {
  for (int i = l; i <= r; i++) cout << a[i] << " ";
  cout << endl;
}
template <class T>
void wt(const T& x) {
  cout << x << endl;
}
template <class T>
void wt(const T& x, char c) {
  cout << x << c;
}
template <class T>
void wt(const T& x, const string& s) {
  cout << x << s;
}
template <class T>
void wt(const T& x, int rnd) {
  cout << fixed << setprecision(rnd) << x << endl;
}
inline long long lowbit(long long x) { return (x & (-x)); }
inline void debug() { cout << "###!!!" << endl; }
inline long long read() {
  char c = getchar();
  long long x = 0, f = 1;
  while (c < '0' || c > '9') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') x = 1ll * x * 10 + c - '0', c = getchar();
  return x * f;
}
long long n, k;
long long a[maxn];
int m;
const int N = maxn;
struct Dsu {
  int size, set_num;
  int fa[N], num[N];
  void init(int n) {
    size = set_num = n;
    for (int i = 0; i <= n; i++) fa[i] = i, num[i] = 1;
  }
  int fd(int x) { return x == fa[x] ? x : fa[x] = fd(fa[x]); }
  bool join(int x, int y) {
    int u = fd(x), v = fd(y);
    if (u == v) return 0;
    fa[u] = v;
    num[v] += num[u];
    set_num--;
    return 1;
  }
  bool same(int x, int y) { return fd(x) == fd(y); }
} dd;
int main() {
  while (cin >> n >> m) {
    dd.init(n);
    std::vector<pair<int, int> > v;
    for (int i = 1; i <= m; i++) {
      int l, r, op;
      cin >> op >> l >> r;
      if (op) {
        for (int i = r; i >= l; i--) dd.join(i, l);
      } else
        v.push_back(pair<int, int>(l, r));
    }
    for (auto d : v) {
      if (dd.same(d.first, d.second)) {
        wt("NO");
        return 0;
      }
    }
    int ans = 1e6;
    wt("YES");
    for (int i = 1; i <= n; i++) {
      if (dd.fa[i] == i) ans--;
      wt(ans);
    }
  }
  return 0;
}