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>

#define F first
#define S second
#define pii pair<int, int>
#define pb push_back

using namespace std;

typedef long long ll;
typedef long double ld;

const int N = 1e6 + 10, mod = 1e9 + 7;

int dp[N], ps[N];

int main()
{
	int n, sum; cin >> n;
	dp[1] = n;
	dp[2] = (ll)n * n % mod;
	sum = (dp[1] + dp[2]) % mod;

	for (int i=3; i<=n; i++)
	{
		dp[i] = (((ll)sum - dp[i - 2] + mod) + (ll)(n - 1) * (n - 1)) % mod;
		dp[i] += (n - i + 2), dp[i] %= mod;
		sum += dp[i], sum %= mod;
	}
	cout << dp[n] << endl;
}
