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 maxn 1000005
#define Mod 1000000007
#define Val(x) (((long long)x) % Mod)
using namespace std;
int dp[maxn];
int cal(int n) {
	return Val((1 + n - 1) * (n-1) / 2);
}
int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin >> n;
	
	int sum = 0 , coe = 0;
	for(int i=1;i<=n;i++) {
		dp[i] = Val(sum + 1);
		coe = Val(coe + dp[i-2]);
		sum = Val(sum + coe);
	}
		
	int ans = Val(dp[n] * (n-1) + 1);
	for(int i=1;i<n;i++)
		ans = Val(Val(dp[i] * (n-1)) * n + ans);
	cout << ans << endl;
	return 0;
}
