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())
mod=10**9+7
DP=[0]*(N*2+5)
X=[0]*(N*2+5)
Y=[0]*(N*2+5)
C=0
Y[0]=-1
for i in range(N):
  C=(C+X[i])%mod
  DP[i]=(C-Y[i])%mod
  Y[i+2]=DP[i]
  X[i+1]=(X[i+1]+DP[i])%mod
  X[i+N+2]=(X[i+N+2]-DP[i])%mod
for i in range(N,N*2+2):
  C=(C+X[i])%mod
  DP[i]=(C-Y[i])%mod
P=sum(DP[N:])
for i in range(N-1):
  P=(P+DP[i]*(N-1)*(N-1))%mod
print(P)