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;
const int N = 1e6+10;
const int mod = 1000000007;
int n,ans[N],sum;
int main() {
	scanf("%d",&n);
	ans[n] = n;
	ans[n-1] = (long long)n * n % mod;
	for(int i = n - 2; i >= 1; i--) {
		sum = (sum + ans[i + 3]) % mod;
		ans[i] = ans[i + 1];
		ans[i] = (ans[i] + (long long)(n - 1) * (n - 1) % mod) % mod;
		ans[i] = (ans[i] + sum) % mod;
		ans[i] = (ans[i] + i + 1) % mod;
	}
	printf("%d\n",ans[1]);
	return 0;
}