# #P3070. Fibonacci

# Fibonacci

## Description

In the Fibonacci integer sequence, *F*_{0} = 0, *F*_{1} = 1, and *F _{n}* =

*F*

_{n}_{ − 1}+

*F*

_{n}_{ − 2}for

*n*≥ 2. For example, the first ten terms of the Fibonacci sequence are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

An alternative formula for the Fibonacci sequence is

.

Given an integer *n*, your goal is to compute the last 4 digits of *F _{n}*.

## Input

The input test file will contain multiple test cases. Each test case consists of a single line containing n (where 0 ≤ *n* ≤ 1,000,000,000). The end-of-file is denoted by a single line containing the number −1.

## Output

For each test case, print the last four digits of *F _{n}*. If the last four digits of

*F*are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print

_{n}*F*mod 10000).

_{n}```
0
9
999999999
1000000000
-1
```

```
0
34
626
6875
```

## Hint

As a reminder, matrix multiplication is associative, and the product of two 2 × 2 matrices is given by

.

Also, note that raising any 2 × 2 matrix to the 0th power gives the identity matrix:

.