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:
from functools import cmp_to_key


def comp(x, y):
    if x[0] != y[0]:
        return x[0] - y[0]
    return y[1] - x[1]


n, m = map(int, input().split())
ans = [-1 for i in range(n)]
tps = []
tans = [n]
for i in range(m):
    t, l, r = map(int, input().split())
    tps.append((l, r, t))
tps.sort(key=cmp_to_key(comp))
for i in range(m - 1):
    if tps[i][1] >= tps[i + 1][1] and tps[i][2] and not tps[i + 1][2]:
        print("NO")
        exit(0)
for l, r, t in tps:
    if t:
        ans[l - 1:r - 1] = [1 for i in range(r - l)]
for i in range(1, n):
    tans.append(0)
    tans[i] = tans[i - 1] + ans[i - 1]
for l, r, t in tps:
    if t:
        if not all(tans[i] <= tans[i + 1] for i in range(l - 1, r - 1)):
            print("NO")
            exit(0)
    else:
        if all(tans[i] <= tans[i + 1] for i in range(l - 1, r - 1)):
            print("NO")
            exit(0)
print("YES")
for i in tans:
    print(i, end=' ')