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C. Vasya And Array

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya has an array $$$a_1, a_2, \dots, a_n$$$.

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 $$$r_i$$$ ($$$0 \le t_i \le 1, 1 \le l_i < r_i \le n$$$) and it means:

- if $$$t_i=1$$$ then subbarray $$$a_{l_i}, a_{l_i + 1}, \dots, a_{r_i}$$$ is sorted in non-decreasing order;
- if $$$t_i=0$$$ then subbarray $$$a_{l_i}, a_{l_i + 1}, \dots, a_{r_i}$$$ 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 $$$m$$$ ($$$2 \le n \le 1000, 1 \le m \le 1000$$$).

Each of the next $$$m$$$ lines contains three integers $$$t_i$$$, $$$l_i$$$ and $$$r_i$$$ ($$$0 \le t_i \le 1, 1 \le l_i < r_i \le n$$$).

If $$$t_i = 1$$$ then subbarray $$$a_{l_i}, a_{l_i + 1}, \dots , a_{r_i}$$$ is sorted. Otherwise (if $$$t_i = 0$$$) subbarray $$$a_{l_i}, a_{l_i + 1}, \dots , a_{r_i}$$$ 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 $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — 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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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