Given an array A of N elements, you can pick at most one element of the array and increment or decrement it by any value. The task is to maximize the AND of the resulting array.

Note: AND of the array is defined as the bitwise AND(&) of all the array elements.

Constraints: 2 ≤ N ≤ 2 * 105 0 ≤ A[i] ≤ 2 * 109