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())

if n == 1:
    print(1)
else:
    res_v = [0]*(n + 1)
    res_v_cumsum = [0]*(n + 1)
    res_v[0] = 0
    res_v[1] = 1
    res_v[2] = 1
    res_v_cumsum[0] = 0
    res_v_cumsum[1] = 1
    res_v_cumsum[2] = 2

    M = 1000000007

    for k in range(3, n):
        res_v[k] = (1 + res_v_cumsum[k-1] - res_v[k-2]) % M
        res_v_cumsum[k] = (res_v_cumsum[k-1] + res_v[k]) % M
    #print(res_v)
    print((((res_v_cumsum[n-2] * (((n-1) * (n-1)) % M)) % M) + ((res_v_cumsum[n-1] * (n-1)) % M) + n + (n-1)*(n-1)%M) % M)