## M00PAIR - 0 0 Pairs

A sequence consisting of one digit, the number 1 is initially written into a computer. At each successive time step, the computer simultaneously transforms each digit 0 into the sequence 1 0 and each digit 1 into the sequence 0 1.

So, after the first time step, the sequence 0 1 is obtained; after the second, the sequence 1 0 0 1, after the third, the sequence 0 1 1 0 1 0 0 1 and so on.

How many pairs of consecutive zeroes will appear in the sequence after n steps?

### Input

Clarification for this Problem: The Range of inputs is from 1 to 999 in some order and in particular not in ascending order

### Output

For each input n print the number of consecutive zeroes pairs that will appear in the sequence after n steps.

### Sample

```Sample Input 12 3 45
Sample output 01 135```

## Code Examples

### #1 Code Example with Python Programming

```Code - Python Programming```

``````dp = [0] * 1005
dp[1] = 0
dp[2] = 1
for i in range(3, 1005):
dp[i] = dp[i - 1] + 2 * dp[i - 2]
while True:
try:
N = int(input())
print(dp[N])
except EOFError:
exit()``````
Copy The Code &

Input

cmd
1
2
3
4
5

Output

cmd
0
1
1
3
5