CF981E Addition on Segments

Description

Grisha come to a contest and faced the following problem. You are given an array of size $ n $ , initially consisting of zeros. The elements of the array are enumerated from $ 1 $ to $ n $ . You perform $ q $ operations on the array. The $ i $ -th operation is described with three integers $ l_i $ , $ r_i $ and $ x_i $ ( $ 1 \leq l_i \leq r_i \leq n $ , $ 1 \leq x_i \leq n $ ) and means that you should add $ x_i $ to each of the elements with indices $ l_i, l_i + 1, \ldots, r_i $ . After all operations you should find the maximum in the array. Grisha is clever, so he solved the problem quickly. However something went wrong inside his head and now he thinks of the following question: "consider we applied some subset of the operations to the array. What are the possible values of the maximum in the array?" Help Grisha, find all integers $ y $ between $ 1 $ and $ n $ such that if you apply some subset (possibly empty) of the operations, then the maximum in the array becomes equal to $ y $ .

Input Format

N/A

Output Format

N/A

Explanation/Hint

Consider the first example. If you consider the subset only of the first query, the maximum is equal to $ 1 $ . If you take only the second query, the maximum equals to $ 2 $ . If you take the first two queries, the maximum becomes $ 3 $ . If you take only the fourth query, the maximum becomes $ 4 $ . If you take the fourth query and something more, the maximum becomes greater that $ n $ , so you shouldn't print it. In the second example you can take the first query to obtain $ 1 $ . You can take only the second query to obtain $ 2 $ . You can take all queries to obtain $ 3 $ . In the third example you can obtain the following maximums: - You can achieve the maximim of $ 2 $ by using queries: $ (1) $ . - You can achieve the maximim of $ 3 $ by using queries: $ (2) $ . - You can achieve the maximim of $ 5 $ by using queries: $ (1, 2) $ . - You can achieve the maximim of $ 6 $ by using queries: $ (3) $ . - You can achieve the maximim of $ 8 $ by using queries: $ (1, 3) $ . - You can achieve the maximim of $ 9 $ by using queries: $ (2, 3) $ .