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 rev(a, l, r):
	j = 0
# 	print(l, r)
	for i in range(l, r + 1,2):
		a[l + j], a[r - j] = a[r - j], a[l + j]
		j += 1

n,m = map(int, input().split())
pairs = []
pairs2 = []
for i in range(m):
    t, l, r = map(int,input().split())
    l -= 1
    r -= 1
    if(t == 1):
    	pairs.append([l, -r])
    else:
        pairs2.append([l, r])
pairs.sort()

actual_pairs = []
for i in range(len(pairs)):
    # print(actual_pairs, pairs[i][0])
    if(len(actual_pairs) > 0 and actual_pairs[-1][1] >= pairs[i][0]):
    	actual_pairs[-1][1] = max(actual_pairs[-1][1], -pairs[i][1])
    	continue
    actual_pairs.append([pairs[i][0], -pairs[i][1]])
    # print(actual_pairs[-1][1], pairs[i][0])

# print(actual_pairs)

arr = [(n - i) for i in range(n)]

for i in range(len(actual_pairs)):
	rev(arr, actual_pairs[i][0], actual_pairs[i][1])

for i in pairs2:
	flag = False
	max1 = 0
	for j in range(i[0], i[1]):
		max1 = max(arr[j], max1)
		if(max1 > arr[j + 1]):
			flag = True
			break
	if(not flag):
		print("NO")
# 		print(*arr)
		exit()
print("YES")
print(*arr)