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;

typedef long long lli;
const int MOD=1e9+7,MAXN=1000000;

int n;
int main() {
	scanf("%d",&n);

	int ps=n-1,ans=n,pr=n,ppr=1;
	for(int i=2;i<=n;i++) {
		ans = (pr + ps + 1ll*(n-1)*(n-1)%MOD)%MOD;
		ps = (1ll*ps + ppr - 1 + MOD)%MOD;
		ppr = pr;
		pr = ans;
		pr = ans;
	}
	printf("%d\n",ans);
	
	return 0;
}
