问题链接：Fibonacci Freeze

The Fibonacci numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...) are defined by the recurrence:

      F0 = 0

      F1 = 1

      Fi = Fi−1 + Fi−2 for all i ≥ 2

  Write a program to calculate the Fibonacci Numbers.

Input

The input to your program would be a sequence of numbers smaller or equal than 5000, each on a separate line, specifying which Fibonacci number to calculate.

Output

Your program should output the Fibonacci number for each input value, one per line.

Sample Input

5

7

11

Sample Output

The Fibonacci number for 5 is 5

The Fibonacci number for 7 is 13

The Fibonacci number for 11 is 89

程序说明：

  用二维数组来表示大数，并且采用万进制，高位在每一行的右边（低位在左边）。

C++:

/* UVA495 Fibonacci Freeze */
 
#include <bits/stdc++.h>
 
using namespace std;
 
const int N = 5000;
const int N2 = 300;
const int BASE = 1e4;
int fib[N+ 1][N2 + 1];
 
void maketable()
{
    memset(fib, 0, sizeof(fib));
 
    fib[0][0] = 0;
    fib[1][0] = 1;
    for ( int i = 2 ; i <= N ; i++ ) {
        for ( int j = 0 ; j <= N2 ; j++ )
            fib[i][j] = fib[i-2][j] + fib[i-1][j];
        for ( int j = 0 ; j <= N2 ; j++ ) {
            fib[i][j+1] += fib[i][j] / BASE;
            fib[i][j] %= BASE;
        }
    }
}
 
int main()
{
    maketable();
 
    int n;
    while(~scanf("%d", &n)) {
        int i = N2;
        while ( i >= 1 && !fib[n][i] )
            i --;
        printf("The Fibonacci number for %d is ", n);
        printf("%d", fib[n][i--]);
        while ( i >= 0 )
            printf("%04d", fib[n][i--]);
        printf("\n");
    }
 
    return 0;
}