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
dp[0] = 1
tot = 1
for i in range(1,n):
    if(i==1):
        dp[i] = tot
    else:
        dp[i] = tot - dp[i-2]
    dp[i] %= mod
    tot += dp[i]
    tot %= mod

ans = 0
for i in range(n-1):
    ans += dp[i] * ((n-1)**2 + min(n-1, i+2))
    ans %= mod

ans += dp[-1]*n
ans %= mod
print(ans)