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 sys     
import math as mt
import bisect
#input=sys.stdin.readline
#t=int(input())
t=1
def ncr_util():
    inv[0]=inv[1]=1
    fact[0]=fact[1]=1
    for i in range(2,300001):
        inv[i]=(inv[i%p]*(p-p//i))%p
    for i in range(1,300001):
        inv[i]=(inv[i-1]*inv[i])%p
        fact[i]=(fact[i-1]*i)%p
#def solve():
    
    
    
    
for _ in range(t):
    #n=int(input())
    #n1=int(input())
    #s=input()
    #n=int(input())
    n,m=(map(int,input().split()))
    #n1=n
    #a=int(input())
    #b=int(input())
    #a,b,c,r=map(int,input().split())
    #x2,y2=map(int,input().split())
    #n=int(input())
    #s=input()
    #s1=input()
    #p=input()
    #l=list(map(int,input().split()))
    #l2=list(map(int,input().split()))
    #l=str(n)
    #l.sort(reverse=True)
    #l2.sort(reverse=True)
    #l1.sort(reverse=True)
    ans=[-1]*(n+1)
    l1=[]
    for i in range(m):
        x,y,z=(map(int,input().split()))
        if x==1:
            for i in range(y+1,z+1):
                ans[i]=0
        else:
            l1.append([y,z])
    flag=True
    ans[0]=1010
    #print(ans)
    for i in range(1,n+1):
        ans[i]+=ans[i-1]
    #print(ans,sorted(ans[5:7]))
    for i in range(len(l1)):
        if  ans[l1[i][0]:l1[i][1]+1]==sorted(ans[l1[i][0]:l1[i][1]+1]):
            flag=False
            break
    if flag:
        print("YES")
        print(*ans[1:])
    else:
        print("NO")