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
def main():
    mod = 10**9+7
    n = int(input())
    a, b, c, p = 1, 1, n, n-1
    for i in range(n-1):
        p = (p+a-1) % mod
        a, b, c = b, c, ((n-1)*(n-1)+p+c) % mod
    print(c)


main()
