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
#!/usr/bin/env python3
# -*- coding: utf-8 -*-

from random import *

def readln():
    _res = list(map(int,str(input()).split(' ')))
    return _res

p = 1000000000 + 7

n = readln()[0]
f = [0 for i in range(0,n+10)]
f[1] = n
f[2] = n * n
s = f[:]
s[2] = f[1] + f[2]
for i in range(3,n+1):
    f[i] = f[i-1] + (n - 1) * (n - 1)
    f[i] = f[i] + s[i - 3] + (n - i + 2)
    f[i] = f[i] % p
    s[i] = s[i - 1] + f[i]
    s[i] = s[i] % p
print(f[n])
