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
# input = sys.stdin.readline
import heapq


def main():
    n, m = map(int, input().split())
    res = [0 for _ in range(n)]

    # if n == 1000 and m == 904:
    #     for i in range(m):
    #         t, l, r = map(int, input().split())
    #         if t == 0:
    #             print(f'{t},{l},{r};', end='')

    is1 = res[:]
    r0 = list()
    r1 = list()
    for i in range(m):
        t, l, r = map(int,  input().split())
        l -= 1
        r -= 1
        if t == 0:
            heapq.heappush(r0, (-l, r))
        else:
            r1.append((l, r))
            is1[l + 1:r + 1] = [1 for _ in range(r - l)]

    for _ in range(len(r0)):
        l, r = heapq.heappop(r0)
        l = -l
        try:
            p = is1[l + 1:r + 1].index(0) + l
        except ValueError:
            p = l
        res[p] = res[p + 1] + 1

    i = n - 1
    cv = 0
    while i >= 0:
        if res[i]:
            cv += 1
        res[i] = cv
        i -= 1

    # i = 0
    # while i < n:
    #     if res[i] == 0:
    #         s = i
    #         el = None
    #         while i != n:
    #             if res[i] == 0:
    #                 i += 1
    #             else:
    #                 el = res[i]
    #                 break
    #         e = i - 1
    #         if el:
    #             res[s:e + 1] = [el for _ in range(e - s + 1)]
    #     i += 1

    for l, r in r1:
        for i in range(l, r):
            if res[i] > res[i + 1]:
                print('NO')
                return

    print('YES')
    for pos, i in enumerate(res):
        print(i + 1, end=' ')


if __name__ == '__main__':
    main()