Problem Statement

We have a long, thin piece of paper whose thickness can be ignored. We perform the following operation $100$ times: lift the right end, fold it so that it aligns with the left end using the center as a crease. After completing the $100$ folds, we unfold the paper back to its original state. At this point, there are $2^{100} - 1$ creases on the paper, and these creases can be classified into two types: mountain folds and valley folds. The figure below represents the state after performing the operation twice, where red solid lines represent mountain folds and red dashed lines represent valley folds.

About mountain and valley folds A crease is a mountain fold if it is folded so that the back sides of the paper come together at the crease. A crease is a valley fold if it is folded so that the front sides of the paper come together at the crease.

You are given a sequence $A = (A_1, A_2, \dots, A_N)$ of $N$ non-negative integers. Here, $0 = A_1 < A_2 < \dots < A_N \leq 10^{18}$.

For each integer $i$ from $1$ through $2^{100} - A_N - 1$, define $f(i)$ as follows:

• The number of $k = 1, 2, \dots, N$ such that the $(i + A_k)$-th crease from the left is a mountain fold.

Find the maximum value among $f(1), f(2), \dots, f(2^{100} - A_N - 1)$.

Constraints

• $1 \leq N \leq 10^3$
• $0 = A_1 < A_2 < \dots < A_N \leq 10^{18}$

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the answer in one line.