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
P = 10 ** 9 + 7
N = int(input())
k = (N-1) ** 2 % P + 2
a, b, c = 1, 0, 0
ans = 0
for i in range(N-1):
    ans += a * (k + min(i, N-3))
    ans %= P
    a, b, c = a + b, b + c, a
    if a >= P: a -= P
    if b >= P: b -= P

ans += N * a
ans %= P
print(ans)