Anthony is obsessed with sorting algorithms. After mastering a couple different sorting algorithms, he is now learning how to solve more unconventional sorting problems. Initially, there is an array of size . Anthony can perform the following operation any number of times: change an element of to any arbitrarily large non-negative integer. Let the array be the prefix bitwise XOR array of . Formally, . Please tell Anthony the minimum number of operations to sort in non-decreasing order.

#### Constraints

##### Subtask 1 [20%]

##### Subtask 2 [80%]

No additional constraints.

#### Input Specification

The first line contains the integer .

The next line contains space-separated integers, representing the array .

#### Output Specification

Output the minimum number of operations to make nondecreasing.

#### Sample Input

```
3
2 2 4
```

#### Sample Output

`1`

#### Explanation for Sample

operation can be performed by changing the first element to , making nondecreasing.

## Comments