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
#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
const int MD = 1e9+7;
long long n, a[1000005];
int main(){
	scanf("%lld", &n);
	a[1] = n; a[2] = (n*n + n) % MD; a[3] = 3*n*n % MD;
	for(int i = 4; i <= n; i++) a[i] = (a[i-1]*2 - a[i-2] + a[i-3] + 3 - i + n*(n-1)) % MD;
	printf("%lld\n", (a[n] - a[n-1] + MD) % MD);
}