p03766 AtCoder Regular Contest 071 - Infinite Sequence
How many infinite sequences a_1, a_2, ... consisting of {{1, ... ,n}} satisfy the following conditions?

* The n-th and subsequent elements are all equal. That is, if n \leq i,j, a_i = a_j.
* For every integer i, the a_i elements immediately following the i-th element are all equal. That is, if i < j < k\leq i+a_i, a_j = a_k.



Find the count modulo 10^9+7.

Constraints

* 1 \leq n \leq 10^6

Input

Input is given from Standard Input in the following format:


n


Output

Print how many sequences satisfy the conditions, modulo 10^9+7.

Examples

Input

2


Output

4


Input

654321


Output

968545283
```python
n = int(input())
dp = [0] * (n+1)
mod = 10**9+7
dp[0] = n
dp[1] = n*n
SUM = n+n*n
for i in range(2,n):
  dp[i] = (n-1)*(n-1) + n-i+1+SUM-dp[i-2]
  dp[i] %= mod
  SUM += dp[i]
  SUM %= mod
print(dp[n-1])
```