Even more sequences of bits

Please compute the number of different sequences of length $n$, made up of only zeroes and ones, and with no more than two consecutive ones.

Input

Input consists of several cases, each with a natural number $n$ between 0 and $10^9$.

Output

For every case, print the number of different sequences of $n$ bits that do not have more than two consecutive ones, modulo $10^9 + 7$.

Hint

A matrix can be powered to a natural number $x$ with only $\Theta(\log x)$ products of matrices.

Problem information

Author: Pol Mauri

Generation: 2026-01-25T12:01:35.030Z

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