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==1:
  print(1)
  exit()
mod=10**9+7
dp=[0]*(n+1)
S=[0]*(n+1)
dp[0]=1
dp[1]=1
dp[2]=1
S[0]=1
for i in range(n):
  if i+1>=3:
    dp[i+1]=2*dp[i]-dp[i-1]+dp[i-2]
  dp[i+1]%=mod
  S[i+1]=S[i]+(n-1)*dp[i]
  S[i+1]%=mod
ans=S[n]
for i in range(1,n):
  ans+=((n-1)**2)*dp[i-1]
  ans%=mod
print(ans)
#print(S)
#print(dp)