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 main():
    n, m = map(int, input().split())
    l0 = []; r0 = []; l1 = []; r1 = []
    for _ in range(m):
        ti, li, ri = map(int, input().split())
        if ti:
            l1.append(li); r1.append(ri)
        else:
            l0.append(li); r0.append(ri)
    segments = []
    for i in range(len(l1)):
        new_segments = []
        to_add = [l1[i], r1[i]]
        for segment in segments:
            if to_add[0] > segment[1] or to_add[1] < segment[0]:
                new_segments.append(segment)
            else:
                to_add[0] = min(to_add[0], segment[0])
                to_add[1] = max(to_add[1], segment[1])
        new_segments.append(to_add)
        segments = new_segments
    segments.sort(key = lambda x : x[0])
    #print(segments)
    for i in range(len(l0)):
        for segment in segments:
            if l0[i] >= segment[0] and r0[i] <= segment[1]:
                print("NO")
                return
    print("YES")
    sz = 0
    z = 1001
    p = []
    for i in range(1, n + 1):
        if sz == len(segments) or i <= segments[sz][0]:
            z -= 1
            p.append(z)
        elif i < segments[sz][1]:
            p.append(z)
        else:
            sz += 1
            p.append(z)
            #z -= 1
    print(*p)
main()