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 ll long long
#define f(i, x, n) for (int i = x; i < (int)(n); ++i)

int dp[1000001], md = 1e9 + 7;

int main(){
	int n;
	scanf("%d", &n);
	dp[1] = n;
	int al = n;
	f(i, 2, n + 1){
		dp[i] = ((ll)(n - 1) * (n - 1) + al - dp[i - 2] + md) % md;
		int z = min(n - 1, n - 1 - (i - 3));
		dp[i] += z;
		if (dp[i] >= md)dp[i] -= md;
		al += dp[i];
		if (al >= md)al -= md;
	}
	printf("%d\n", dp[n]);
}
