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:
# # n=int(input())
# # ls=list(map(int,input().split()))
# # rs=list(map(int,input().split()))
# # x=[]
# # p=1000000007
# # def fac(a,b):
# #     bs=[1,b]
# #     for i in range(30):
# #         bs.append(bs[-1]*bs[-1]%p)
# #     ans=1
# #     for i in range(32):
# #         if ((p-2)>>i)&1==1:
# #             ans=(ans*bs[i])%p
# #     return (ans*a)%p
# # def overlap(l1,r1,l2,r2):
# #     ov=(max(l1,l2),min(r1,r2))
# #     if ov[0]>ov[1]:
# #         return 0
# #     return fac(ov[1]-ov[0]+1,r2-l2+1)
# #
# #
# # ps=[]
# # ps2=[]
# # for i in range(1,n):
# #     ps.append(overlap(ls[i-1],rs[i-1],ls[i],rs[i]))
# #     ps2.append(ps[-1]*ps[-1]%p)
# # print(ps)
# # print(ps2)
# #
# # sm=sum(ps)%p
# # ans=sm*sm%p+3*sm%p+p-sum(ps2)%p+1
# # print(ans%p)
# #
#
# import sys
#
# class Tee(object):
#     def __init__(self, *files):
#         self.files = files
#     def write(self, obj):
#         for f in self.files:
#             f.write(obj)
#             f.flush() # If you want the output to be visible immediately
#     def flush(self) :
#         for f in self.files:
#             f.flush()
#
# f = open('/Users/joe/out.txt', 'w')
# original = sys.stdout
# sys.stdout = Tee(sys.stdout, f)
# print("test")  # This will go to stdout and the file out.txt
#
# #use the original
# # sys.stdout = original
# print ("11111111")  # Only on stdout
# xxx=1
# f.close()

def gns():
    return list(map(int, input().split()))
n, m = gns()
inc = []
dec = []
for i in range(m):
    t, a, b = gns()
    a -= 1
    b -= 1
    if t == 0:
        dec.append((a, b))
    else:
        inc.append((a, b))

inc.sort()
ans = [-1] * n
if len(inc) == 0:
    print('YES')
    print(' '.join(map(str,list(reversed(range(1, n + 1))))))
    quit()

s, t = inc[0]
cur = 1

to = [[inc[0][0]]]
for i in range(len(inc)):
    ss, tt = inc[i]
    if ss <= t:
        t = max(t, tt)
    else:
        to[-1].append(t)
        to.append([ss])
        t = tt
to[-1].append(t)
# print(to)

for ss, tt in to:
    for i in range(ss, tt + 1):
        ans[i] = cur
    cur += 1

cur = n + 1
i = 0
while i < n:
    if ans[i] == -1:
        ans[i] = cur
        cur -= 1
        i += 1
        continue
    st = ans[i]
    for j in range(i, n):
        if ans[j] != st:
            break
        ans[j] = cur
    else:
        break
    cur -= 1
    i = j


def check(a, b):
    for i in range(a, b):
        if not ans[i] <= ans[i + 1]:
            return True
    return False


for a, b in dec:
    if not check(a, b):
        print('NO')
        quit()
print('YES')
print(' '.join(map(str, ans)))