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:

if __name__ == '__main__':
    n, m = map(int, input().split())
    srt = []
    nsrt = []
    for i in range(m):
        t, l, r = map(int, input().split())
        if t == 1:
            srt.append((l - 1, r - 1))
        else:
            nsrt.append((l - 1, r - 1))

    ans = []
    for i in range(n, 0, -1):
        ans.append(i)

    if not srt:
        print("YES")
        print(" ".join(list(map(str, ans))))
        exit(0)

    srt.sort()
    inters = []
    beg, end = srt[0]
    for l, r in srt:
        if l <= end:
            end = max(end, r)
        else:
            inters.append((beg, 0, end))
            beg, end = l, r
    inters.append((beg, 0, end))

    for l, r in nsrt:
        inters.append((l, 1, r))

    inters.sort()

    b1, e1 = -1, -1
    for l, o, r in inters:
        if o == 0:
            b1, e1 = l, r
            tmp = ans[l:r + 1]
            tmp.sort()
            ans[l:r + 1] = tmp
            # for i in range(l, r + 1):
            #     ans[i] = str(i + 1 - l + 1000)
        else:
            if b1 != -1 and e1 != -1 and b1 <= l and r <= e1:
                print("NO")
                exit(0)

    print("YES")
    print(" ".join(list(map(str, ans))))