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>
#define MOD 1000000007
#define sqr(x) ((ll)(x) * (x))
typedef long long ll; 
ll dp[1000005], sum; 
int main()
{
	// freopen("ARC071-F.in", "r", stdin); 
	int n; 
	scanf("%d", &n); 
	dp[1] = n; 
	dp[2] = sqr(n) % MOD; 
	for (int i = 3; i <= n; i++)
	{
		dp[i] = (dp[i - 1] + sqr(n - 1) + sum + n - i + 2) % MOD; 
		(sum += dp[i - 2]) %= MOD; 
	}
	printf("%lld\n", dp[n]);
	return 0;
}
