You are given an array $A$ of even length $N$ consisting of non-negative integers. You need to make each element of the array equal to zero, by doing some number of moves (possibly zero).

In a single move, you can choose two integers, $l$ and $r$, so $1 \leq l \leq r \leq N$. Let $x = A[l] ⊕ A[l+1] ⊕ A[l+2] ... A[r]$, where ⊕ represents xor operator. Then, replace the whole subarray with $x$. In other words, assign $A[i] = x$ for $l ≤ i ≤ r$.

Print the minimum number of moves required to make the entire array zero.

Input format

• The first line contains a single integer $N$ – the length of array $A$.
• The next line contains $N$ space-separated integers representing the elements of the array $A$.

Output format
Output a single integer – the answer.

Constraints

$1 \leq N \leq 10^6\\ \\0\leq A[i] \le 10^9\\ \\N\;is\;even$