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 sys, os, math
from collections import Counter, defaultdict
import bisect
from sys import stdin, stdout
from itertools import repeat, izip

# n, k = map(int, raw_input().split())
# da = map(int, raw_input().split())
# db = map(int, raw_input().split())


def main():
    inf = int(1e12)
    n, m = map(int, raw_input().split())
    so = []
    la = []
    for i in range(m):
        t, l, r = map(int, raw_input().split())
        if t == 1:
            so.append([l, r])
        else:
            la.append([l, r])
    so.append([1,1])
    la.sort()
    so.sort()
    reso = [so[0]]
    for i, j in so[1:]:
        if i <= reso[-1][-1]:
            reso[-1][-1] = max(reso[-1][-1], j)
        else:
            reso.append([i, j])
    ans = [0 for i in range(n + 1)]
    total = 0
    for i, j in reso:
        total += j - i + 1
    idx = 100000
    for i, j in reversed(reso):
        for k in range(i, j + 1):
            ans[k] = idx
        idx += 2000
    for i in range(1, n + 1):
        if ans[i] == 0:
            ans[i] = idx
            idx -= 1
        else:
            idx = ans[i] - 1
    for i, j in la:
        if i == j:
            print "NO"
            exit(0)
        for ki, kj in reso:
            if i >= ki and j <= kj:
                print "NO"
                exit(0)
    print 'YES'
    print ' '.join(map(str, ans[1:]))


main()