AT_arc227_c [ARC227C] Follow the Letters

You are given a string $ S $ of length $ N $ consisting of lowercase English letters. Let $ S_i $ denote the $ i $ -th character of $ S $ . There are $ N $ islands arranged in a circle, numbered island $ 1 $ , island $ 2 $ , $ \ldots $ , island $ N $ in clockwise order. In particular, the island clockwise-adjacent to island $ N $ is island $ 1 $ . The character $ S_i $ is written on island $ i $ . Initially, there is one person on each island. You can perform the following operation zero or more times. - Choose one character $ c $ that appears in $ S $ . Every person departs from the island they are currently on and moves one island at a time in the clockwise direction. Each person stops as soon as they first arrive, after departing, at an island on which the character $ c $ is written. Even if the island a person is currently on has the character $ c $ written on it, that person still departs. Let $ K $ be the minimum possible number of islands that have one or more people on them after all operations are finished. Find $ K $ , and a sequence of operations that makes the number of islands with one or more people equal to $ K $ after the operations. Under the constraints of this problem, it can be proved that there always exists a sequence of operations of length at most $ 10^6 $ that makes the number of islands with one or more people equal to $ K $ .

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

Let $ L $ be an integer representing the number of operations, and let $ X $ be a string representing the sequence of operations. Output in the following format: > $ K $ $ L $ $ X $ If $ L=0 $ , output the third line as an empty line. $ L $ must satisfy $ 0 \le L \le 10^6 $ . $ X $ must be a string of length $ L $ consisting of characters that appear in $ S $ , and the $ i $ -th character of $ X $ represents the character chosen in the $ i $ -th operation. After performing the operations according to the sequence $ X $ , the number of islands with one or more people must be $ K $ . If multiple outputs satisfy the conditions, you may output any of them.

### Sample Explanation 1 If we perform the operation choosing the character `b`, everyone gathers on the island on which the character `b` is written. The number of islands with people becomes $ 1 $ , and this is the minimum. ### Sample Explanation 2 By choosing `a` first and then `b`, everyone gathers on the same island. The number of islands with people becomes $ 1 $ , and this is the minimum. ### Sample Explanation 3 No matter which operation is performed, each person moves to the next island in the clockwise direction. Therefore, the number of islands with people is always $ 4 $ , so $ K=4 $ . In this sample output, no operation is performed. ### Constraints - $ 1 \le N \le 1000 $ - $ S $ is a string of length $ N $ consisting of lowercase English letters. - $ N $ is an integer.