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:
from collections import defaultdict


def solve(ss, us, n):
    st = []
    ss = sorted(ss)
    for s, e in ss:
        if len(st) == 0:
            st.append((s, e))
        else:
            if s <= st[-1][1]:
                if e <= st[-1][1]:
                    continue
                else:
                    st[-1] = st[-1][0], e
            else:
                st.append((s, e))
    for s, e in us:
        for ss, ee in st:
            if s >= ss and e <= ee:
                return None
    res = [1] * n
    nex = {}
    for ss, ee in st:
        nex[ss] = ee
        for i in xrange(ss + 1, ee + 1):
            res[i] = res[i - 1] + 1
            nex[i] = ee
    ii = []
    for s, e in us:
        if s in nex:
            ii.append(nex[s])
        else:
            ii.append(s)
    a = 3000
    for i in sorted(ii):
        res[i] = a
        a -= 1
    return res


import random


def aaaaa():
    a = random.randint(0, 9)
    b = random.randint(a + 1, 10)
    return a, b


#
# ss = [(0, 7), (1, 5)]
# us = [(2, 8), (8, 10)]
# print solve(ss, us, 11)
#
# for t in xrange(100000):
#     ss = [aaaaa(), aaaaa(), aaaaa(), aaaaa()]
#     us = [aaaaa(), aaaaa(), aaaaa(), aaaaa()]
#     r = solve(ss, us, 11)
#     if r == None:
#         continue
#     for s in ss:
#         z = r[s[0]: s[1] + 1]
#         if z == sorted(z):
#             continue
#         else:
#             print ss, us
#     for u in us:
#         z = r[u[0]: u[1] + 1]
#         if z == sorted(z):
#             print ss, us
#             break
# print "HAHA"

n, m = map(int, raw_input().split(" "))
ss, us = [], []
for _ in xrange(m):
    t, l, r = map(int, raw_input().split(" "))
    if t == 1:
        ss.append((l - 1, r - 1))
    else:
        us.append((l - 1, r - 1))
aa = solve(ss, us, n)
if aa == None:
    print "NO"
else:
    print "YES"
    for i in xrange(0, len(aa)):
        z = aa[i]
        print z,
    print