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 LL;

const int maxn = 1000009;
const int MOD = 1e9+7;
LL f[maxn], n, sum;

int main(){
	scanf("%lld", &n);
	f[1] = n; f[2] = n*n%MOD;
	for (int i=3; i<=n; i++){
		f[i] = (f[i-1] + (n-1)*(n-1) + sum + (n-i+2)) % MOD;
		sum = (sum + f[i-2]) % MOD;
	}
	printf("%lld\n", f[n]);
	return 0;
}