In the Fibonacci integer sequence, F0 = 0, F1 = 1, and Fn = Fn− 1 + Fn− 2 for n ≥ 2. For example, the first ten terms of the Fibonacci sequence are:
An alternative formula for the Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … Given an integer n, your goal is to compute the last 4 digits of Fn.
输入格式
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.
输出格式
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 Fn mod 10000).
输入样例
复制
0
9
999999999
1000000000
-1
输出样例
复制
0
34
626
6875
数据范围与提示
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：