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:
# a = list(map(int, input().strip().split()))
# from sys import stdout stdout.flush()
# from functools import cmp_to_key def cmp(x,y): if x+y>y+x 1 else -1
# sorted(a, key = cmp_to_key(cmp))

# isprime = [True] * MAX_SIZE     prime = [] 
# isprime[0] = isprime[1] = False
#     for i in range(2, N):  
#        if isprime[i] == True: prime.append(i)
#        j = 0
#        while (j < len(prime) and i * prime[j] < N): 
#            isprime[i * prime[j]] = False  
#            j+=1

#def extended_euclid_gcd(a, b):
#    s = 0; old_s = 1
#    t = 1; old_t = 0
#    r = b; old_r = a

#    while r != 0:
#        quotient = old_r//r
#        old_r, r = r, old_r - quotient*r
#        old_s, s = s, old_s - quotient*s
#        old_t, t = t, old_t - quotient*t
#    return [old_r, old_s, old_t] #gcd, x, y for ax+by=gcd

n,m = list(map(int, input().strip().split()))
are = [False] * n

unos = []
zeros = []
for i in range(m):
    t,l,r = list(map(int, input().strip().split()))
    if t == 1:
        unos.append((l-1,r))
    else:
        zeros.append((l-1,r))
unos.sort()
c = 10000000
for i in range(len(unos)):
    l, r = unos[i]
    if are[l] == False:
        for k in range(l, r):
            are[k] = c
        c -= 10000
    else:
        storer = are[l]
        for k in range(l, r):
            are[k] = storer

if are[0] == False:
    are[0] = 20000000
for i in range(1,n):
    if are[i] == False:
        are[i] = are[i-1]-1

flagg = True
for i in range(len(zeros)):
    l, r = zeros[i]
    b = are[l:r]
    b.sort()
    if b == are[l:r]:
        flagg = False

if flagg:
    print("YES")
    print(" ".join(map(str, are)))
else:
    print("NO")