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())
lsttttt=[1]*(n+10)
L0=[]
L1=[]
pp=[0]*(n-1)
for ooo in range(m):
    t,l,r=map(int,input().split())
    if(t==1):
        L1.append((l-1,r-1))
    else:
        L0.append((l-1,r-1))
 
L1=sorted(L1)
L0=sorted(L0)


for i in range(0,len(L1)):
    l=L1[i][0]
    r=L1[i][1]

    for j in range(l,r):
        pp[j]=1




flag1=1
for i in range(0,len(L0)):
    l=L0[i][0]
    r=L0[i][1]

    flag=0
    for j in range(l,r):
        if(pp[j]==-1):
            flag=1
            continue
        elif(pp[j]==0):
            pp[j]=-1
            flag=1
    if(flag==0):
        flag1=0

if(flag1==0):
    print('NO')
else:

    k=100000
    lsttttt[0]=100000
    for i in range(0,len(pp)):
        if(pp[i]==1):
            lsttttt[i+1]=lsttttt[i]+1
        elif(pp[i]==-1):
            lsttttt[i+1]=lsttttt[i]-1
        else:
            lsttttt[i+1]=lsttttt[i]

    print('YES')
    for i in range(n):
        print(lsttttt[i],end=" ")
    print(" ")