Mystical Fibonacci Sequence

You are given a positive integer t. Your task is to compute the t-th term of the Mystical Fibonacci Sequence defined as follows:

\( F(t) = \begin{cases} 1, & \text{if } t = 1 \text{ or } t = 2, \\ F(t-1) + F(t-2) + t^2, & \text{if } t \ge 3. \end{cases} \)

Since the values can be very large, output the result modulo \(10^9+7\).

Note: All formulas are given in LaTeX format. The input is taken from standard input and the result is printed to standard output.

inputFormat

The input consists of a single integer t (1 ≤ t ≤ 10⁵), representing the position in the Mystical Fibonacci Sequence.

Input is read from stdin.

outputFormat

Output a single integer which is the t-th term of the Mystical Fibonacci Sequence modulo \(10^9+7\>.

Output should be written to stdout.

## sample

1

1

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