1187_C. Vasya And Array
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
```python
"""609C"""
# import math
# import sys
def  main():
	n,m = map(int,input().split())
	l = []
	s = []
	r = []
	d = [0]*n
	for _ in range(m):
		a,b,c = map(int,input().split())
		s.append(a)
		b-=1
		l.append(b)
		c-=1
		r.append(c)
		if a==1:
			d[b]+=1
			d[c]-=1
	dx = [-1]*(n-1)
	add = 0
	for i in range(n):
		add+=d[i]
		if add>0:
			dx[i] = 0
	res = [0]*n
	res[0]=n
	for i in range(1,n):
		res[i]=res[i-1]+dx[i-1]
	nxt = [0]*n
	nxt[n-1]=n-1
	for i in range(n-2,-1,-1):
		if res[i]<=res[i+1]:
			nxt[i]=nxt[i+1]
		else:
			nxt[i]=i
	# print(d)
	# print(dx)
	# print(res)
	# print(nxt)
	for i in range(m):
		if s[i] != (nxt[l[i]]>=r[i]):
			# print(i,s[i],nxt[l[i]]>=r[i])
			print("NO") 
			return
	print("YES")
	for x in res:
		print(x,end=' ')
	print()

main()
# def test():
# 	t= int(input())
# 	while t:
# 		main()
# 		t-=1
# test()
```