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=[int(i) for i in input().split()]
q1=[]
q0=[]
arr=[-1]*n
for _ in range(m):
    q=[int(i) for i in input().split()]
    if(q[0]==0):
        q0.append(q)
    else:
        q1.append(q)
for i in range(len(q1)):
    l=q1[i][1]
    r=q1[i][2]
    if(arr[l-1]==-1):
        if(arr[r-1]==-1):
            for j in range(l-1,r):
                arr[j]=i
        else:
            for j in range(l-1,r):
                arr[j]=arr[r-1]
    else:
        if(arr[r-1]==-1):
            for j in range(l-1,r):
                arr[j]=arr[l-1]
        elif(arr[r-1]!=arr[l-1]):
            for j in range(l,r-1):
                arr[j]=arr[l-1]
            u=r
            while(arr[u]==arr[r-1]):
                arr[u]=arr[l-1]
                u+=1
                if u==n:
                    break
            arr[r-1]=arr[l-1]
flag=True
for i in q0:        
    l=i[1]-1
    r=i[2]-1
    if(arr[l]==arr[r] and arr[l]!=-1):
        flag=False
        break
if flag:
    p=-2
    j=1
    for i in range(1,n+1):
        if(arr[-i]==-1):
            j+=1
            arr[-i]=j
        elif(arr[-i]==p):
            arr[-i]=j
        else:
            p=arr[-i]
            j+=1
            arr[-i]=j
    print("YES")
    print(*arr)
else:
    print("NO")