CF1743D.Problem with Random Tests

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.

给你一个由 $n$ 个字符组成的字符串 $s$，其中每个字符均为 0 或 1。

$s$ 的一个子串是指其字符的一个连续子序列。

你需要从 $s$ 中选出两个子串（允许相交、可以相同、也可以不相交——即任意两个子串均可）。选定后，你将按如下方式计算该子串对的值：

• 设 $s_1$ 为第一个子串，$s_2$ 为第二个子串，$f(s_i)$ 表示以 $s_i$ 作为二进制表示所对应的整数（例如，若 $s_i$ 为 11010，则 $f(s_i) = 26$）；
• 该值即为 $f(s_1)$ 与 $f(s_2)$ 的按位或（bitwise OR）结果。

请计算你能得到的最大可能值，并以不带前导零的二进制形式输出。

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.

第一行包含一个整数 $n$ —— 字符串 $s$ 的字符个数。

第二行包含字符串 $s$ 本身，它恰好由 $n$ 个字符组成，每个字符为 0 或 1。

本题中所有非示例测试用例均为随机生成：字符串 $s$ 的每个字符独立选取；对每个字符而言，其为 1 的概率恰好为 $\frac{1}{2}$。

本题共有 $40$ 个测试用例。其中第 $1$ 至 $3$ 个测试用例为示例；第 $4$ 至 $40$ 个测试用例为随机生成。在第 $4$ 至 $10$ 个测试用例中，$n = 5$；在第 $11$ 至 $20$ 个测试用例中，$n = 1000$；在第 $21$ 至 $40$ 个测试用例中，$n = 10^6$。

本题禁止使用 Hack。

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

输出不带前导零的二进制表示下你能得到的最大可能值。

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.

在第一个例子中，你可以选择子字符串 11010 和 101。$f(s_1) = 26$，$f(s_2) = 5$，它们的按位或为 $31$，而 $31$ 的二进制表示为 11111。

在第二个例子中，你可以选择子字符串 1110010 和 11100。