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 solve():
    n, m = input().split()
    n = int(n)
    m = int(m)
    sorted_bounds = []
    unsorted_bounds = []
    for i in range(m):
        t, l, r = input().split()
        if int(t) == 1:
            sorted_bounds.append([int(l), int(r)])
        else:
            unsorted_bounds.append([int(l), int(r)])

    for i in range(len(unsorted_bounds)):
        for j in range(len(sorted_bounds)):
            if is_inside(sorted_bounds[j], unsorted_bounds[i]):
                print("NO")
                quit()


    r = [0]*(n-1)

    for b in sorted_bounds:
        r[b[0]-1:b[1]-1] = [1]*(b[1] - b[0])

    a = [0]*n
    current = n
    a[0] = current
    for i in range(n - 1):
        if r[i] == 0:
            current -= 1
        a[i + 1] = current

    for b in unsorted_bounds:
        if a[b[0]-1] == a[b[1]-1]:
            print("NO")
            quit()

    print('YES')
    print(" ".join(map(str, a)))

def is_inside(f, s):
    return f[0] <= s[0] and s[1] <= f[1]

solve()