或最大值 - المسألة

#4280. 或最大值

الإحصائيات

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

bobo 有一个序列 $a_1, a_2, \dots, a_n$。他想选择 $k$ 个连续的元素，并最大化值 $S$，其中 $S$ 定义为这些元素的最大值与按位或（bitwise OR）之和。

对于所有 $1 \le k \le n$，求出 bobo 能达到的最大值 $S$。

输入格式

第一行包含一个整数 $n$ ($1 \le n \le 10^5$)。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$ ($0 \le a_i < 2^{16}$)。

输出格式

输出 $n$ 个整数，其中第 $i$ 个整数表示当 $k = i$ 时的最大值 $S$。

样例

样例输入 1

3
1 0 2

样例输出 1

4
4
5

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