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 = 2e3 + 5;
const long long mod = 1e9 + 7;
struct node {
  int l, r;
} p[2][maxn], p1[maxn];
int ans[maxn];
int fa[maxn];
int finds(int x) {
  if (fa[x] == x) return x;
  return fa[x] = finds(fa[x]);
}
int main() {
  int n, m;
  scanf("%d", &n);
  scanf("%d", &m);
  int cnt0 = 0, cnt1 = 0;
  for (int i = (1); i <= (m); i++) {
    int t, l, r;
    scanf("%d", &t);
    scanf("%d", &l);
    scanf("%d", &r);
    if (t == 0)
      p[t][++cnt0] = (node){l, r};
    else
      p[t][++cnt1] = (node){l, r};
  }
  for (int i = (1); i <= (cnt1); i++) fa[i] = i;
  for (int i = (1); i <= (cnt1); i++)
    for (int j = (1); j <= (cnt1); j++) {
      if (j == i) continue;
      if ((p[1][i].l >= p[1][j].l && p[1][i].r <= p[1][j].r) ||
          (p[1][i].l <= p[1][j].l && p[1][i].r >= p[1][j].r) ||
          (p[1][i].r >= p[1][j].l && p[1][i].r <= p[1][j].r) ||
          (p[1][i].l >= p[1][j].l && p[1][i].l <= p[1][j].r)) {
        int x = finds(i), y = finds(j);
        if (x != y) fa[x] = y;
      }
    }
  for (int i = (1); i <= (cnt1); i++) p1[i].l = 1e9, p1[i].r = -1e9;
  for (int i = (1); i <= (cnt1); i++) {
    int x = finds(i);
    p1[x].l = min(p1[x].l, p[1][i].l);
    p1[x].r = max(p1[x].r, p[1][i].r);
  }
  for (int i = (1); i <= (cnt1); i++) {
    if (p1[i].l > p1[i].r) continue;
    for (int j = (1); j <= (cnt0); j++)
      if (p[0][j].l >= p1[i].l && p[0][j].r <= p1[i].r) {
        puts("NO");
        return 0;
      }
    for (int o = (p1[i].l); o <= (p1[i].r - 1); o++) ans[o] = 1;
    ans[p1[i].r] = 200002;
  }
  int now = 200000;
  for (int i = (1); i <= (n); i++) {
    if (ans[i]) {
      now = 200000;
      continue;
    }
    ans[i] = now--;
  }
  puts("YES");
  for (int i = (1); i <= (n); i++) printf("%d ", ans[i]);
}