infiniteseq

Title

Problem Statement

How many infinite sequences a1, a2, ... consisting of {{1, ... ,n}} satisfy the following conditions?

  • The n-th and subsequent elements are all equal. That is, if n ≤ i,j, ai = aj.
  • For every integer i, the ai elements immediately following the i-th element are all equal. That is, if i < j < k≤ i+ai, aj = ak.

Find the count modulo 109+7.

Constraints

  • 1 ≤ n ≤ 106

Input

Input is given from Standard Input in the following format:

n

Output

Print how many sequences satisfy the conditions, modulo 109+7.

Sample Input 1

2

Sample Output 1

4

The four sequences that satisfy the conditions are:

  • 1, 1, 1, ...
  • 1, 2, 2, ...
  • 2, 1, 1, ...
  • 2, 2, 2, ...

Sample Input 2

654321

Sample Output 2

968545283

Submitting .cpp to 'infiniteseq'


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Compile Errors


							
Time Limit: 1 Seconds
Memory Limit: 256MB
No. of ACs: 4
Your best score: 0
Source: AtCoder Regular Contest 071

Subtask Score
1 100
2 0