You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 4.0 seconds
Memory limit: 512.0 MB

# Problem
For a sequence of integers $$$[x_1, x_2, \dots, x_k]$$$, let's define its decomposition as follows:

Process the sequence from the first element to the last one, maintaining the list of its subsequences. When you process the element $$$x_i$$$, append it to the end of the first subsequence in the list such that the bitwise AND of its last element and $$$x_i$$$ is greater than $$$0$$$. If there is no such subsequence in the list, create a new subsequence with only one element $$$x_i$$$ and append it to the end of the list of subsequences.

For example, let's analyze the decomposition of the sequence $$$[1, 3, 2, 0, 1, 3, 2, 1]$$$:

- processing element $$$1$$$, the list of subsequences is empty. There is no subsequence to append $$$1$$$ to, so we create a new subsequence $$$[1]$$$;
- processing element $$$3$$$, the list of subsequences is $$$[[1]]$$$. Since the bitwise AND of $$$3$$$ and $$$1$$$ is $$$1$$$, the element is appended to the first subsequence;
- processing element $$$2$$$, the list of subsequences is $$$[[1, 3]]$$$. Since the bitwise AND of $$$2$$$ and $$$3$$$ is $$$2$$$, the element is appended to the first subsequence;
- processing element $$$0$$$, the list of subsequences is $$$[[1, 3, 2]]$$$. There is no subsequence to append $$$0$$$ to, so we create a new subsequence $$$[0]$$$;
- processing element $$$1$$$, the list of subsequences is $$$[[1, 3, 2], [0]]$$$. There is no subsequence to append $$$1$$$ to, so we create a new subsequence $$$[1]$$$;
- processing element $$$3$$$, the list of subsequences is $$$[[1, 3, 2], [0], [1]]$$$. Since the bitwise AND of $$$3$$$ and $$$2$$$ is $$$2$$$, the element is appended to the first subsequence;
- processing element $$$2$$$, the list of subsequences is $$$[[1, 3, 2, 3], [0], [1]]$$$. Since the bitwise AND of $$$2$$$ and $$$3$$$ is $$$2$$$, the element is appended to the first subsequence;
- processing element $$$1$$$, the list of subsequences is $$$[[1, 3, 2, 3, 2], [0], [1]]$$$. The element $$$1$$$ cannot be appended to any of the first two subsequences, but can be appended to the third one.

The resulting list of subsequences is $$$[[1, 3, 2, 3, 2], [0], [1, 1]]$$$.

Let $$$f([x_1, x_2, \dots, x_k])$$$ be the number of subsequences the sequence $$$[x_1, x_2, \dots, x_k]$$$ is decomposed into.

Now, for the problem itself.

You are given a sequence $$$[a_1, a_2, \dots, a_n]$$$, where each element is an integer from $$$0$$$ to $$$3$$$. Let $$$a[i..j]$$$ be the sequence $$$[a_i, a_{i+1}, \dots, a_j]$$$. You have to calculate $$$\sum \limits_{i=1}^n \sum \limits_{j=i}^n f(a[i..j])$$$.

## Input Format
The first line contains one integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 3$$$).

## Output Format
Print one integer, which should be equal to $$$\sum \limits_{i=1}^n \sum \limits_{j=i}^n f(a[i..j])$$$.

## Examples
```input
8
1 3 2 0 1 3 2 1
```
```output
71
```
-----
```input
5
0 0 0 0 0
```
```output
35
```

Now solve the problem and return the code.