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 <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#define LL long long
using namespace std;
const int Maxn = 1000000 + 100, Mod = 1000000007;
LL N;
LL F[Maxn];
int main()
{
	scanf("%lld", &N);
	F[1] = N;
	F[2] = (N * N) % Mod;
	LL Sum = 0;
	for (int i = 3; i <= N; ++i)
	{
		F[i] = (F[i - 1] + Sum) % Mod;
		F[i] = (F[i] + ((N - 1) * (N - 1) % Mod)) % Mod;
		F[i] = (F[i] + N - i + 2) % Mod;
		Sum = (Sum + F[i - 2]) % Mod;
	}
	printf("%lld\n", F[N]);
	return 0;
}