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
# -*- coding: utf-8 -*-
mod = 10**9 + 7

n = int(raw_input())

a = [0]*n
x = n - 1
for i in xrange(n - 1, - 1, -1):
    if i == n - 1:
        a[i] = n
    elif i == n - 2:
        a[i] = n*n
    else:
        x -= 1
        x += a[i + 3] if i + 3 < n else 1
        x %= mod
        a[i] += a[i + 1] + (n - 1)*(n - 1) + x
    a[i] %= mod
print a[0]
