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:
import sys
#sys.stdin = open('in', 'r')
#n = int(input())
n,m = map(int, input().split())
a = [1]*n
for i in range(n):
    a[i] = -(n - i)
Ok = True
srt = []
for ti in range(m):
    t,l,r = map(int, input().split())
    l -= 1
    r -= 1
    if t == 1:
        v = abs(a[l])
        for j in range(l, r):
            a[j] = v
        if a[r] > 0:
            over = a[r]
            l = r + 1
            while l < n and a[l] == over:
                a[l] = v
                l += 1
        a[r] = v
    else:
        srt.append((l,r))

for i in range(n):
    if a[i] < 0:
        a[i] = -a[i]

for i in range(len(srt)):
    l,r = srt[i]
    cnt = 0
    for j in range(l, r):
        if a[j] > a[j+1]:
            cnt += 1
            break
    if cnt == 0:
        Ok = False

if Ok:
    print('YES')
    print(' '.join(map(str, a)))
else:
    print('NO')



#sys.stdout.write('YES\n')
#sys.stdout.write(f'{res}\n')
#sys.stdout.write(f'{y1} {x1} {y2} {x2}\n')