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
import sys

n = int(input())
mod = 10 ** 9 + 7

if n == 1:
    print (1)
    sys.exit()

lis = [0] * n
lis[0] = 1
bsum = 0
ans = min(n-1,2) + (n-1) ** 2



for i in range(n-1):

    i += 1

    lis[i] += lis[i-1]

    if i - 3 >= 0:
        bsum += lis[i-3]
        bsum %= mod

    lis[i] += bsum
    lis[i] %= mod

    if i != n-1:

        ans += lis[i] * ((n-1) ** 2)
        ans += lis[i] * min(n-1 , i+2)
        ans %= mod

    

ans += lis[-1] * n
ans %= mod

#print (lis)
print (ans)
