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:
# -*- coding: utf-8 -*-

import math
import collections
import bisect
import heapq
import time
import random
import itertools
import sys
from typing import List

"""
created by shhuan at 2020/1/9 19:50

"""


def merge(s):
    q = []
    for l, r in s:
        if not q:
            q.append((l, r))
        else:
            if l <= q[-1][1]:
                pl, pr = q.pop()
                q.append((pl, max(r, pr)))
            else:
                q.append((l, r))
    return q


def solve(N, M, Q):
    A = [(l, r) for t, l, r in Q if t == 1]
    B = [(l, r) for t, l, r in Q if t == 0]

    A.sort()

    A = merge(A)

    for la, ra in A:
        for lb, rb in B:
            if la <= lb <= rb <= ra:
                print('NO')
                return
    d = [-1 for _ in range(N)]
    for l, r in A:
        for i in range(l+1, r + 1):
            d[i] = 0

    v = N+ 100
    # print(d)
    # print(A)
    ans = [0 for _ in range(N)]
    for i in range(N):
        v += d[i]
        ans[i] = v

    # print(ans)
    for l, r in B:
        if any([ans[i] > ans[i+1] for i in range(l, r)]):
            continue
        else:
            print('NO')
            return

    print('YES')
    print(' '.join(map(str, ans)))






# def test():
#     n = random.randint(2, 10)
#     a = []
#     for i in range(n):
#         l = random.randint(0, 100)
#         r = l + random.randint(0, 100)
#         a.append((l, r))
#     a.sort()
#     print(a)
#     print(merge(a))
#
# test()

N, M = map(int, input().split())
Q = []
for i in range(M):
    t, l, r = map(int, input().split())
    Q.append((t, l-1, r-1))

solve(N, M, Q)