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<cstdio>
#include<algorithm>
using namespace std;
typedef long long i64;

const int MOD = 1000000007;

int N;
i64 dp[1010101];

void add(i64 &a, i64 b)
{
	a = (a + b) % MOD;
}

int main()
{
	scanf("%d", &N);
	dp[N - 1] = N;

	i64 acc = 0;
	for (int i = N - 2; i >= 0; --i) {
		dp[i] = dp[i + 1];
		add(dp[i], (i64)(N - 1) * (N - 1));

		add(acc, dp[i + 3]);
		add(dp[i], acc);
		add(dp[i], min(N - 1, i + 2));
	//	printf("%d: %lld\n", i, dp[i]);
	}
	printf("%lld\n", dp[0]);
	return 0;
}
