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())
container=[0 for i in range(n+1)]
stick=[0 for i in range(n+1)]
maxid=[-1 for i in range(n+1)]
stored=[]
for _ in range(m):
    t,l,r=map(int,input().split())
    if(t==1):
        maxid[l]=max(maxid[l],r)
    else:
        stored.append([l,r])
maxi=0
for i in range(1,n+1):
    maxi=max(maxi,maxid[i])
    if(maxi>=i):
        container[i]=1
    if(maxi==i):
        stick[i]=1
count=1
ans=[0 for i in range(n+1)]
for i in range(n,0,-1):
    ans[i]=count
    if(container[i-1]==1==container[i] and stick[i-1]==0):
        pass
    else:
        count+=1
flag=2
for i in stored:
    flag=0
    for k in range(i[0],i[1]):
        if(ans[k]>ans[k+1]):
            flag=1
            break
    if(flag==0):
        break
if(flag==0):
    print("NO")
else:
    print("YES")
    print(*ans[1:])