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 < 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.

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.

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.