7677번 - Fibonacci 다국어

In the Fibonacci integer sequence, F₀ = 0, F₁ = 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

\[\begin{bmatrix} F_{ n+1 } & F_{ n } \\ F_{ n } & F_{ n-1 } \end{bmatrix}=\begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}^n\]

Given an integer n, your goal is to compute the last 4 digits of F_n.

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.

For each test case, print the last four digits of Fn. If the last four digits of Fn are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print F_n mod 10000).