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 PYTHON):

Solution:
import fileinput
def D(a):print(a)
def main():
    z=0
    N=0
    O=[0]*1024
    B=[0]*1024
    E=[0]*1024
    C=[0]*1024
    T=[0]*1024
    L=0
    for l in fileinput.input():
        z+=1
        if(z<2):
            N=int(l.split(" ")[0])
            O=[0]*N
            for i in range(N):
                O[i]=N-i
                T[i]=i
            continue
        c=int(l.split(" ")[0])
        b=int(l.split(" ")[1])
        e=int(l.split(" ")[2])
        b-=1
        e-=1
        if(c==1):
            T[b]=max(T[b],e)
            continue
        B[L]=b
        E[L]=e
        L+=1
    for i in range(N):
        for j in xrange(i+1,T[i]+1):
            O[j]=O[i]
    for i in xrange(1,N):
        if(C[i]==1):
            O[i]=O[i-1]
    for i in xrange(0,L):
        if(O[B[i]]==O[E[i]]):
            D("NO")
            return
    D("YES")
    s=""
    for i in O:s+=str(i)+" "
    D(s)
main()