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
mod = 1000000007
eps = 10**-9


def main():
    import sys
    input = sys.stdin.readline

    N = int(input())
    ans = [0] * (N+1)
    ans[N] = N
    ans[N-1] = N*N
    S = 0
    for i in range(N-2, 0, -1):
        ans[i] = (ans[i+1] + S + N*(i+1) + (N-1) * (N-i-2))%mod
        S = (S + ans[i+2])%mod
    print(ans[1])
    #print(ans)


if __name__ == '__main__':
    main()
