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 resource
import sys
#resource.setrlimit(resource.RLIMIT_STACK, [0x100000000, resource.RLIM_INFINITY])
#import threading
#threading.Thread(target=main).start()
#threading.stack_size(2**26)
#sys.setrecursionlimit(10**6)
mod=(10**9)+7
#fact=[1]
#for i in range(1,100001):
#    fact.append((fact[-1]*i)%mod)
#ifact=[0]*100001
#ifact[100000]=pow(fact[100000],mod-2,mod)
#for i in range(100000,0,-1):
#    ifact[i-1]=(i*ifact[i])%mod
from sys import stdin, stdout
import bisect
from bisect import bisect_left as bl
from bisect import bisect_right as br
import itertools
import collections
import math
import heapq
#from random import randint as rn
#from Queue import Queue as Q
def modinv(n,p):
    return pow(n,p-2,p)
def ncr(n,r,p):
    t=((fact[n])*((ifact[r]*ifact[n-r])%p))%p
    return t
def ain():
    return map(int,sin().split())
def sin():
    return stdin.readline().strip()
def GCD(x,y):
    while(y):
        x, y = y, x % y
    return x
def isprime(x):
    if(x==1):
        return False
    elif(x<4):
        return True
    for i in range(2,int(math.sqrt(x))+1):
        if(x%i==0):
            return False
    return True
"""**************************************************************************"""
ans=[]
n,m=ain()
b1=[]
b2=[]
for i in range(m):
    t,l,r=ain()
    if(t==1):
        b1.append([l-1,r-1,t])
    else:
        if(l==r):
            print"NO"
            exit()
        b2.append([l-1,r-1,t])
b1.sort()
z=[]
x=-1
y=-1
for i in range(len(b1)):
    if(b1[i][0]>y):
        if(x!=-1 and y!=-1):
            z.append([x,y,0])
        x=b1[i][0]
        y=b1[i][1]
    else:
        y=max(y,b1[i][1])
z.append([x,y,0])
f=[10**9]*n
s=set()
for i in range(len(z)):
    for j in range(z[i][0],z[i][1]):
        s.add((j,j+1))
k=0
for i in range(len(b2)):
    h=0
    for j in range(b2[i][0],b2[i][1]):
        if(f[j+1]<f[j]):
            h=1
            break
        else:
            if((j,j+1) not in s):
                h=1
                for o in range(j+1,n):
                    f[o]-=1
                break
    if(h==0):
        k=1
        break
if(k==1):
    print"NO"
    exit()
print"YES"
for i in range(n):
    f[i]=str(f[i])
stdout.write(" ".join(f))
#for i in range(len(z)):
#stdout.write("\n".join(ans))