Problem with Random Tests

给定一个长度为 $n(n\leq 10^6)$ 的 $01$ 串，要求截取任意两段（可以相交），使得这两段或运算结果最大。**数据随机**。

You are given a string $ s $ consisting of $ n $ characters. Each character of $ s $ is either 0 or 1. A substring of $ s $ is a contiguous subsequence of its characters. You have to choose two substrings of $ s $ (possibly intersecting, possibly the same, possibly non-intersecting — just any two substrings). After choosing them, you calculate the value of the chosen pair of substrings as follows: - let $ s_1 $ be the first substring, $ s_2 $ be the second chosen substring, and $ f(s_i) $ be the integer such that $ s_i $ is its binary representation (for example, if $ s_i $ is 11010, $ f(s_i) = 26 $ ); - the value is the bitwise OR of $ f(s_1) $ and $ f(s_2) $ . Calculate the maximum possible value you can get, and print it in binary representation without leading zeroes.

The first line contains one integer $ n $ — the number of characters in $ s $ . The second line contains $ s $ itself, consisting of exactly $ n $ characters 0 and/or 1. All non-example tests in this problem are generated randomly: every character of $ s $ is chosen independently of other characters; for each character, the probability of it being 1 is exactly $ \frac{1}{2} $ . This problem has exactly $ 40 $ tests. Tests from $ 1 $ to $ 3 $ are the examples; tests from $ 4 $ to $ 40 $ are generated randomly. In tests from $ 4 $ to $ 10 $ , $ n = 5 $ ; in tests from $ 11 $ to $ 20 $ , $ n = 1000 $ ; in tests from $ 21 $ to $ 40 $ , $ n = 10^6 $ . Hacks are forbidden in this problem.

Print the maximum possible value you can get in binary representation without leading zeroes.

5
11010

11111

7
1110010

1111110

4
0000

0

In the first example, you can choose the substrings 11010 and 101. $ f(s_1) = 26 $ , $ f(s_2) = 5 $ , their bitwise OR is $ 31 $ , and the binary representation of $ 31 $ is 11111. In the second example, you can choose the substrings 1110010 and 11100.