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())
dp=[0 for i in range(n+1)]
dp[0]=1
x=(n-1)**2
dp[1]=n
pref=dp[1]
mod=10**9+7
x%=mod
for i in range(2,n+1):
    dp[i]+=x+pref-dp[i-2]+(n-i+2)
    pref+=dp[i]
    pref%=mod
    dp[i]%=mod
        
print(dp[-1])
    