Processing math: 100%
Fibonacci 3 - MarisaOJ: Marisa Online Judge

Fibonacci 3

Time limit: 1000 ms
Memory limit: 256 MB

Given the Fibonacci sequence f0=x,f1=y and fi=fi−1+fi−2 for i>1 with x,y are positive integers. Count the number of pairs (x,y) such that the Fibonacci sequence initialized by these two numbers contains the number k. (k cannot be f0 or f1.)

Input

  • A single positive integer k.

Output

  • Output the number of valid pairs modulo 109+7.

Constraints

  • 1≤k≤109.

Example

Input

6

Output

7

Input

6969

Output

12361