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

# sys.stdin = open('test')

n, m = [int(x) for x in raw_input().split()]
facts = sys.stdin.read().split('\n')

sorted_facts = []
unsorted_facts = []
for i in xrange(m):
    t, l, r = [int(x) for x in facts[i].split()]
    if t:
        sorted_facts.append([l,r])
    else:
        unsorted_facts.append([l,r])

sorted_facts.sort()
unsorted_facts.sort()

if not sorted_facts:
    print 'YES'
    print ' '.join(str(x) for x in reversed(range(1,n+1)))
    exit()
# merge sorted_facts
merged_sorted_facts = []
prev = sorted_facts[0]
for i in xrange(1, len(sorted_facts)):
    if sorted_facts[i][0] <= prev[1]:
        prev[1] = max(prev[1], sorted_facts[i][1])
    else:
        merged_sorted_facts.append(prev)
        prev = sorted_facts[i]
merged_sorted_facts.append(prev)
si = 0
for item in unsorted_facts:
    while si < len(merged_sorted_facts) and merged_sorted_facts[si][1] <= item[0]:
        si += 1
    if si >= len(merged_sorted_facts):
        break
    if merged_sorted_facts[si][0] <= item[0] and merged_sorted_facts[si][1] >= item[1]:
        print 'NO'
        exit()
print 'YES'
prepared =  list(reversed(range(1, n+1)))
for item in merged_sorted_facts:
    prepared[item[0] - 1: item[1]] = [prepared[item[0]-1]] * (item[1] - item[0] + 1)
print ' '.join(str(x) for x in prepared)