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:
def mp():
    return map(int, input().split())
 
def check(l, r):
    return int(a[l:r + 1] == sorted(a[l:r + 1]))
 
n, m = mp()
 
q = [0] * m
for qq in range(m):
    t, l, r = mp()
    l, r = l - 1, r - 1
    q[qq] = [l, r, t]
q.sort()
 
 
a = [0 for i in range(n)]
u = [0 for i in range(n)]
fail = False
 
for qq in range(m):
    l, r, t = q[qq]
    if t == 0:
        if u[l] == 0:
            if l != 0 and u[l - 1] != 0:
                a[l] = a[l - 1]
                u[l] = 1
            else:
                a[l] = r - l + 1
                u[l] = 1
        for i in range(l + 1, r + 1):
            a[i] = a[i - 1] - 1
            u[i] = 1
 
#print(a)
for qq in range(m):
    l, r, t = q[qq]
    if t == 1:
        i = l
        while i < n and u[i] == 0:
            i += 1
        if i == n:
            x = 1
        else:
            x = a[i]
        a[l] = x
        u[l] = x
        for i in range(l + 1, r + 1):
            if a[i - 1] > a[i]:
                a[i] = a[i - 1]
                u[i] = 1
 
mn = min(a)
if mn < 1:
    mn = abs(mn) + 1
    for i in range(n):
        a[i] += mn
 
fail = False
for qq in range(m):
    l, r, t = q[qq]
    if t != check(l, r):
        fail = True
        break
 
if fail:
    print('NO')
else:
    print('YES')
    for i in a:
        print(i, end = ' ')