B. Cat, Fox and the Lonely Array

Today, Cat and Fox found an array 𝑎 consisting of 𝑛 non-negative integers.

Define the loneliness of 𝑎 as the smallest positive integer 𝑘 (1≤𝑘≤𝑛) such that for any two positive integers 𝑖 and 𝑗 (1≤𝑖,𝑗≤𝑛−𝑘+1), the following holds:

𝑎𝑖|𝑎𝑖+1|…|𝑎𝑖+𝑘−1=𝑎𝑗|𝑎𝑗+1|…|𝑎𝑗+𝑘−1,

where 𝑥|𝑦 denotes the bitwise OR of 𝑥 and 𝑦. In other words, for every 𝑘 consecutive elements, their bitwise OR should be the same. Note that the loneliness of 𝑎 is well-defined, because for 𝑘=𝑛 the condition is satisfied.Cat and Fox want to know how lonely the array 𝑎 is. Help them calculate the loneliness of the found array.