AT_abc456_g [ABC456G] Count Holidays

Takahashi is creating a work schedule for $ N $ days by designating each day as a workday or a holiday. You are given a string $ S $ of length $ N $ representing the constraints on work days. If the $ i $ -th character of $ S $ is `x`, day $ i $ must be a workday. If it is `.`, day $ i $ can be either a workday or a holiday. There are $ 2^q $ valid work schedules satisfying the constraints, where $ q $ is the number of `.` characters in $ S $ . For each $ k=1,2,\dots,N $ , solve the following problem: > Among the $ 2^q $ valid work schedules satisfying the constraints, find the number, modulo $ 998244353 $ , of schedules in which the longest consecutive block of holidays is exactly $ k $ days.

The input is given from Standard Input in the following format: > $ N $ $ S $

Output $ N $ lines. The $ i $ -th line should contain the answer for $ k=i $ .

### Sample Explanation 1 Denoting holidays as `o`, the valid work schedules are as follows: - $ k=1 $ : `oxxxx`, `oxoxx`, `oxoxo`, `oxxox`, `oxxxo`, `xxoxx`, `xxoxo`, `xxxox`, `xxxxo` - $ k=2 $ : `oxoox`, `oxxoo`, `xxoox`, `xxxoo` - $ k=3 $ : `oxooo`, `xxooo` ### Constraints - $ N $ is an integer between $ 1 $ and $ 2 \times 10^5 $ , inclusive. - $ S $ is a string of length $ N $ consisting of `.`, `x`.