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

n, m = list(map(int, sys.stdin.readline().strip().split()))
C = []
D = []
for i in range (0, m):
    t, l, r = list(map(int, sys.stdin.readline().strip().split()))
    l = l - 1
    r = r - 1
    if t == 1:
        C.append([l,r])
    else:
        D.append([l,r])
C.sort()
x = len(C)
E = []
i = 0

while i < x:
    a = C[i][0]
    b = C[i][1]
    i = i + 1
    if i != x:
        while C[i][0] <= b:
            b = max([b, C[i][1]])
            i = i + 1
            if i == x:
                break
    E.append([a,b])

v = True
for d in D:
    for e in E:
        if d[0] >= e[0] and d[1] <= e[1]:
            v = False

if v == False:
    print("NO")
else:
    L = [10000-i for i in range (0, n)]
    for e in E:
        for i in range (e[0]+1,e[1]+1):
            L[i] = L[i-1]
    L = list(map(str,L))
    print("YES")
    print(" ".join(L))