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:
import math


#5 4 4 4 3
n,m=map(int,input().split())
ans=[-(i+1) for i in range(n)]
query=[]
chec=[]
cnt=1
for i in range(m):
    x,y,z=map(int,input().split())
    if(x==1):
        query.append([y,z])
    else:
        chec.append([y,z])
        continue;
query.sort()

for i in range(len(query)):
    t=query[i]
    maxa=-math.inf
    for j in range(t[0]-1,t[1]):
        maxa=max(maxa,ans[j])

    for j in range(t[0]-1,t[1]):
        ans[j]=maxa

flag=0
glag=0

for i in range(len(chec)):
    x=chec[i]
    flag=1
    for j in range(x[0],x[1]):
      
        if(ans[j]<ans[j-1]):
            flag=0
            break;

    if(flag==1):
        glag=1
        break;

            
if(glag==0):
    print('YES')
    r=min(ans)
    for i in range(len(ans)):
        ans[i]+=abs(r)+1
    print(*ans)
else:
    print('NO')