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:
n, m = map(int, input().split())
a = (n - 1) * [-1]
zeros = []
flag = 0
for i in range(m):
    x = list(map(int, input().split()))
    if x[1] == 1:
        if x[0] == 1:
            flag = 1
    if x[0] == 0:
        zeros.append(x)
    else:
        for j in range(x[1], x[2]):
            a[j - 1] = 1
for l in range(len(zeros)):
    for p in range(zeros[l][1], zeros[l][2]):
        if a[p - 1] == -1 or a[p - 1] == 0:
            a[p - 1] = 0
            break
        elif p == zeros[l][2] - 1:
            print('NO')
            exit()
print('YES')
for k in range(n - 1):
    if k == 0 and a[k] == 0:
        a[k] = 5000
    elif a[k] == -1:
        a[k] = 2000
    elif a[k] == 0:
        a[k] = a[k - 1] - 1
    elif a[k] == 1:
        a[k] = a[k - 1] + 10
if flag == 0:
    print(a[0] + 1, *a)
else:
    print(a[0] - 1, *a)