CF1187C.Vasya And Array

Vasya 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 $r_i$ ($0 \le t_i \le 1, 1 \le l_i \lt r_i \le n$) 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.

瓦西里有一个数组 $a_1, a_2, \dots, a_n$。

你并不知道这个数组，但他告诉了你关于该数组的 $m$ 条信息。第 $i$ 条信息是一个三元组 $t_i$、$l_i$ 和 $r_i$（其中 $0 \le t_i \le 1$，$1 \le l_i \lt r_i \le n$），其含义如下：

• 若 $t_i = 1$，则子数组 $a_{l_i}, a_{l_i + 1}, \dots, a_{r_i}$ 是非递减有序的；
• 若 $t_i = 0$，则子数组 $a_{l_i}, a_{l_i + 1}, \dots, a_{r_i}$ 不是非递减有序的。当且仅当该子数组中存在至少一对相邻元素，使得前者大于后者时，称该子数组不是非递减有序的。

例如，若 $a = [2, 1, 1, 3, 2]$，则他可能给出如下三条信息：$t_1 = 1,\, l_1 = 2,\, r_1 = 4$（子数组 $[a_2, a_3, a_4] = [1, 1, 3]$ 是有序的）；$t_2 = 0,\, l_2 = 4,\, r_2 = 5$（子数组 $[a_4, a_5] = [3, 2]$ 是无序的）；以及 $t_3 = 0,\, l_3 = 3,\, r_3 = 5$（子数组 $[a_3, a_4, a_5] = [1, 3, 2]$ 是无序的）。

你并不知道数组 $a$ 的具体取值。请找出任意一个满足所有给定信息的数组。

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 $r_i$ ($0 \le t_i \le 1, 1 \le l_i \lt r_i \le n$).

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.

第一行包含两个整数 $n$ 和 $m$（$2 \le n \le 1000$，$1 \le m \le 1000$）。

接下来的 $m$ 行每行包含三个整数 $t_i$、$l_i$ 和 $r_i$（$0 \le t_i \le 1$，$1 \le l_i \lt r_i \le n$）。

若 $t_i = 1$，则子数组 $a_{l_i}, a_{l_i + 1}, \dots , a_{r_i}$ 是有序的；否则（即 $t_i = 0$），子数组 $a_{l_i}, a_{l_i + 1}, \dots , a_{r_i}$ 是无序的。

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.

如果不存在满足这些条件的数组，则仅在一行中输出 NO（字母大小写任意）。

如果存在解，则首先输出 YES（字母大小写任意）；第二行输出 $n$ 个整数 $a_1, a_2, \dots, a_n$（其中 $1 \le a_i \le 10^9$），即满足所有给定条件的数组 $a$。若存在多个满足条件的数组，输出任意一个即可。