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:
def get_compressed(facts):
	compressed_facts = dict()
	for fact in facts:
		if fact[0] == 0:
			continue
		start, end = fact[1], fact[2]
		to_remove = []
		skip = False
		for compressed in compressed_facts:
			start_compressed, end_compressed = compressed_facts[compressed]
			if start <= end_compressed and end > end_compressed:
				to_remove.append(compressed)
				start = min(start, start_compressed)
			elif end >= start_compressed and start < start_compressed:
				to_remove.append(compressed)
				end = max(end, end_compressed)
			elif start >= start_compressed and end <= end_compressed:
				skip = True
				break
		if skip:
			continue

		compressed_facts[str(start) + ',' + str(end)] = [start, end]		
		for x in to_remove:
			del compressed_facts[x]

	return compressed_facts

def solve(n, facts):
	compressed_facts = get_compressed(facts)
	# Verify that no 0s are entirely inside 1s
	for fact in facts:
		if fact[0] == 1:
			continue
		for compressed in compressed_facts.values():
			if fact[1] >= compressed[0] and fact[2] <= compressed[1]:
				return None

	a = n * [None]
	for fact in compressed_facts.values():
		start = 10**8
		size = fact[1] - fact[0] + 1
		for i in range(size):
			# This is fine due to the limits on the problem (n < 1000)
			a[fact[0] - 1 + i] = start - (10000 * fact[0]) + i
	for i in range(n):
		if a[i] is None:
			if i == 0:
				a[i] = 10**9 - 1
			else:
				a[i] = a[i-1] - 1
	return a

n, num_facts = map(int, input().split(' '))
facts = []
for _ in range(num_facts):
	facts.append(list(map(int, input().split(' '))))

sol = solve(n, facts)
if sol is None:
	print('NO')
else:
	print('YES')
	print(' '.join(map(str, sol)))