Or Max

bobo has a sequence $a\_1, a\_2, \dots, a\_n$. He would like to choose $k$ consecutive elements and maximize the value $S$ that is defined as their maximum plus their bitwise or.

For all $1 \leq k \leq n$, find the maximal value bobo can achieve.

The first line contains an integer $n$ ($1 \leq n \leq 10^5$).

The second line contains $n$ integers $a\_1, a\_2, \dots, a\_n$ ($0 \leq a\_i < 2^{16}$).

$n$ integers, where the $i$-th integer is maximal $S$ for $k=i$.