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
from itertools import accumulate
N, M = map(int, input().split())
TLR = [tuple(map(int, input().split())) for _ in range(M)]

TLR.sort(reverse = True)

table = [False]*(N+1)

for i in range(M):
    t, l, r = TLR[i]
    l -= 1
    r -= 1
    if not t:
        break
    table[l] += 1
    table[r] -= 1
    if i == M-1:
        i += 1
stp = i

table = list(accumulate(table))

table = [1 if t > 0 else 0 for t in table[:-1]]
table += [0]
col = [-1]*N
ctr = 10000
for i in range(N):
    if table[i-1] == 0:
        ctr -= 1
    if table[i-1] == 1 or table[i] == 1:
        col[i] = ctr
for i in range(stp, M):
    _, l, r = TLR[i]
    l -= 1
    r -= 1
    if col[l] == col[r] > 0:
        break
else:
    print('YES')
    Ans = [10000]*N
    for i in range(N):
        if col[i] < 0 or col[i-1] != col[i]:
            Ans[i] = Ans[i-1] - 1
        else:
            Ans[i] = Ans[i-1]
    print(*Ans)
    sys.exit()
print('NO')