CF2206I Growth Factor

You are given an integer $ n $ and a sequence of integers $ a_1, a_2, \ldots, a_n $ . Your task is to determine the number of integer sequences $ (b_1, b_2, \ldots, b_n) $ such that the following conditions are satisfied: - $ 1 \leq b_i \leq a_i $ for each $ i $ ( $ 1 \le i \le n $ ). - $ b_i $ is a factor of $ b_{i+1} $ for each $ i $ ( $ 1 \le i \le n-1 $ ). Two sequences are considered different if they differ in at least one position. Since the number of such sequences may be large, compute the answer modulo $ 998\,244\,353 $ .

The first line of input contains a single integer $ n $ ( $ 1 \le n \le 200\,000 $ ). The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 200\,000 $ ).

Output the number of distinct sequences satisfying the conditions, modulo $ 998\,244\,353 $ .

Explanation for the sample input/output #1 The following are all sequences satisfying the conditions: $ (2,4) $ , $ (2,2) $ , $ (1,4) $ , $ (1,3) $ , $ (1,2) $ , and $ (1,1) $ .