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
n = int(input())
if n <= 3:
  print([n,n**2,n*(2*n-1)][n-1])
  exit()
mod = 10**9+7
dp = [0]*(n+1)
dp[1] = n
dp[2] = n**2
dp[3] = n*(2*n-1)
acc = sum(dp)
for i in range(4,n+1):
  dp[i] = acc-dp[i-2]+(n-1)**2+n-i+2
  dp[i] %= mod
  acc = (acc+dp[i])%mod
print(dp[n])