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,m = map(int, input().split())
a = []
b = []
j = 1
l = [0]*n
for _ in range(m):
    q,w,e  = map(int, input().split())
    if q == 1:
        a += [ [q,w,e] ]
    else:
        b += [ [q,w,e] ]

for x in a:
    if l[x[1]-1] != 0 and l[x[2] - 1] != 0 and l[x[1]-1] != l[x[2] - 1]:
        #print('ok')
        for i in range( x[1]-1,x[2] ):
            l[i] = l[x[1]-1]
        h = x[2] 
        if x[2] != n-1:
            #print('ok')
            mu = l[x[2]]
            
            while h < n and l[h] == mu:
                #print('ok')
                l[h] = l[x[1]-1]
                h+=1
    elif l[x[1]-1] != 0:
        for i in range( x[1]-1,x[2] ):
            l[i] = l[x[1]-1]
    elif l[x[2]-1] != 0:
        for i in range( x[1]-1,x[2]   ):
            l[i] = l[x[2]-1] 
    else:
        for i in range( x[1]-1,x[2] ):
            l[i] = j    
        j += 1

#print(l)
fl=0
for x in b:
    #print(  l[ x[1] - 1] , l[ x[2] - 1] )
    if (l[ x[1] - 1] == l[ x[2] - 1]) and l[ x[1] - 1]  != 0:
        fl = 1
        break
if fl == 0:
    print('YES')
    val = 10**5
    for i in range(n):
        if i == 0 or (l[i] == l[i-1] and l[i] != 0) :
            print(val, end= ' ')
            val+=1
        else:
            val -= 2
            print(val, end = ' ')
            val+=1
else:
    print('NO')