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 ll mod = 1e9+7;

ll n, dt[1000005], cur;

int main()
{
	scanf("%lld",&n);
	dt[0] = 1;
	dt[1] = n;
	dt[2] = n*n % mod;
	cur = 2*n-1;
	for(ll i=3;i<=n;i++) {
		cur += dt[i-1] - dt[i-2] + dt[i-3] - 1;
		cur = (cur%mod+mod)%mod;
		dt[i] = (cur + (n-1)*(n-1)) % mod;
	}
	printf("%lld\n",dt[n]);
}
