AT_arc227_a [ARC227A] Fermat Point of Binary Strings

A string of length $ 2N $ that contains $ N $ occurrences of each of `0` and `1` is called a good string. For good strings $ S $ and $ T $ , let $ \operatorname{dist}(S, T) $ denote the minimum number of swaps required to make $ S $ equal to $ T $ by swapping two adjacent characters of $ S $ zero or more times. You are given good strings $ A $ , $ B $ , and $ C $ . Among all good strings $ X $ , find one that minimizes the value of $$\operatorname{dist}(A, X)+\operatorname{dist}(B, X)+\operatorname{dist}(C, X),$$ and output it together with the minimum value.

The input is given from Standard Input in the following format: > $ N $ $ A $ $ B $ $ C $

Let $ K $ be the minimum value to be found, and let $ X $ be a good string that achieves it. Output $ K $ and $ X $ in the following format: > $ K $ $ X $ If multiple outputs satisfy the conditions, you may output any of them.

### Sample Explanation 1 If we choose `1010` as the good string $ X $ , then $ \operatorname{dist}(A, X) $ , $ \operatorname{dist}(B, X) $ , and $ \operatorname{dist}(C, X) $ are $ 1 $ , $ 0 $ , $ 3 $ , respectively, and their sum is $ 4 $ . The sum of the distances cannot be made smaller than $ 4 $ . ### Sample Explanation 2 Since the three input strings are all equal, choosing the same string as $ X $ makes the sum of the distances $ 0 $ . ### Constraints - $ 1 \le N \le 2 \times 10^5 $ - Each of $ A $ , $ B $ , and $ C $ is a good string of length $ 2N $ . - $ N $ is an integer.