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:
n, m = map(int, input().split())
arr = [k for k in range(n, 0, -1)]
sors = []
nosors = []
for _ in range(m):
    tp, x1, x2 = map(int, input().split())
    x1 -= 1
    x2 -= 1
    if tp == 1:
        remains = []
        incl = False
        for i in range(len(sors)):
            newfl = True
            if sors[i][0] <= x1 and x2 <= sors[i][1]:
                incl = True
                break
            if x1 <= sors[i][0] <= x2:
                x2 = max(x2, sors[i][1])
                newfl = False
            if x1 <= sors[i][1] <= x2:
                x1 = min(x1, sors[i][0])
                newfl = False
            if newfl:
                remains.append(sors[i])
        if incl:
            remains.extend(sors[i:])
        else:
            remains.append([x1, x2])
        sors = remains
    else:
        nosors.append([x1, x2])
sors.sort(key = lambda pair: pair[0])
for sor in sors:
    for i in range(sor[0], sor[1] + 1):
        arr[i] = n - sor[0]
answer = "YES"
for nosor in nosors:
    for sor in sors:
        if nosor[0] >= sor[0] and nosor[1] <= sor[1]:
            answer = "NO"
            break
print(answer)
if answer == "YES":
    print(' '.join(map(str, arr)))