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>
const int MOD = 1000000007;
int N, f[1000001], s[1000001];
int main()
{
	scanf("%d", &N);
	for (int i = 1; i <= N; i++)
	{
		if (i == 1)
			f[i] = N;
		else if (i == 2)
			f[i] = (long long)N * N % MOD;
		else
			f[i] = (f[i - 1] + s[i - 3] + (long long)N * (N - 1) - i + 3) % MOD;
		s[i] = (s[i - 1] + f[i]) %MOD;
	}
	printf("%d\n", f[N]);
	return 0;
}
