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 PYTHON):

Solution:
#!/usr/bin/env python3
# Submit as pypy2

from __future__ import print_function

import sys


try:
    input = raw_input
    range = xrange
except NameError:
    pass


#def debug(*args, **kwargs):
#    print(*args, *('{}={}'.format(k, v) for k, v in kwargs.items()),
#          sep='; ', file=sys.stderr)


# Test code requires python3
# from hypothesis import given
# from hypothesis import strategies as st


# O(N + M log M)
def go(n, runs):
    events = [None]*(2*len(runs))
    for i, (l, r) in enumerate(runs):
        events[2*i] = (l, True)
        events[2*i+1] = (r - 1, False)
    events.sort()
    #debug(events)
    cur = int(1e4)
    ans = [None]*n
    ct = 0
    j = 0
    for i in range(n):
        while j < len(events) and events[j][0] < i:
            j += 1
        while j < len(events) and events[j][0] == i:
            if events[j][1]:
                ct += 1
            else:
                ct -= 1
            j += 1
        #debug(i, j, ct, cur)
        ans[i] = cur
        if not ct:
            cur -= 1
    return ans


# O(N*M) but can be sped up to O(N+M log M)
def check(n, guess, m, facts, ret=True):
    for t, l, r in facts:
        cond = all(guess[i] <= guess[i+1] for i in range(l, r - 1))
        if ret:
            if cond != t:
                return False
        else:
            assert cond == t
    if ret:
        return True


def solve(n, m, facts):
    for t, l, r in facts:
        assert t in (0, 1) and 0 <= l < r <= n
    guess = go(n, [(l, r) for t, l, r in facts if t])
    if not check(n, guess, m, facts):
        return None
    return guess


def main():
    n, m = map(int, input().split())
    facts = [None]*m
    for i in range(m):
        t, l, r = map(int, input().split())
        facts[i] = (t, l-1, r)
    ans = solve(n, m, facts)
    if ans is None:
        print("NO")
    else:
        print("YES")
        print(*ans)


if __name__ == "__main__":
    main()