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:
import sys


def generate_a_at_sorted_positions(n, sorted_segment):
    sorted_segment.sort()

    union_sorted_segment = []
    a = [n - i for i in range(n)]

    if len(sorted_segment) == 0:
        return a

    current_low, max_high = sorted_segment[0]
    for segment in sorted_segment:
        if segment[0] < max_high:
            max_high = max(max_high, segment[1])
        else:
            union_sorted_segment.append((current_low, max_high))
            current_low = segment[0]
            max_high = segment[1]
    union_sorted_segment.append((current_low, max_high))

    for segment in union_sorted_segment:
        for j in range(segment[0]+1, segment[1]):
            a[j] = a[j-1]

    return a


def check_non_sorted_position(a, non_sorted_segment):
    for segment in non_sorted_segment:
        found_decreasing_position = False
        for j in range(segment[0]+1, segment[1]):
            if a[j] < a[j-1]:
                found_decreasing_position = True
        if not found_decreasing_position:
            return False

    return True


if __name__ == '__main__':
    n, m = map(int, sys.stdin.readline().split())
    sorted_segment, other_segment = [], []

    for line in sys.stdin:
        t, low, high = map(int, line.split())
        if t == 1:
            sorted_segment.append((low-1, high))
        else:
            other_segment.append((low-1, high))

    a = generate_a_at_sorted_positions(n, sorted_segment)
    if check_non_sorted_position(a, other_segment):
        print('YES')
        for x in a:
            print(x, end=' ')
    else:
        print('NO')

    sys.stdin.close()