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 PYTHON3):

Solution:
class rel:
	ans=True
	def __init__(self,i,val=0):
		self.i=i
		self.val=val
		self.numb=[0,0]
	def valor1(self,l,r):
		i=l
		while i<r:
			t[i].val=1
			i+=1
	def valor0(self,l,r):
		i=l
		cnt=0
		while i<r:
			if t[i].val==0:
				cnt+=1
			i+=1
		if cnt==0:rel.ans=0
		

t={}
n,m=map(int,input().split())
for i in range(1,n):
	t[i]=rel(i)
a=[]
for i in range(m):
	b,l,r=map(int,input().split())
	if b==1:
		t[1].valor1(l,r)
	else:a.append([l,r])
for l,r in a:
	t[1].valor0(l,r)
if rel.ans==1:
	t[1].numb[0]=3000
	for i in range(1,n):
		if t[i].val==1:
			t[i].numb[1]=t[i].numb[0]+1
			if i<n-1:t[i+1].numb[0]=t[i].numb[1]
		else:
			t[i].numb[1]=t[i].numb[0]-1
			if i<n-1:t[i+1].numb[0]=t[i].numb[1]
	answer=[]
	for i in range(1,n):
		answer.append(t[i].numb[0])
	answer.append(t[n-1].numb[1])
	print("YES")
	print(*answer)
else:
	print("NO")