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 MOD 1000000007
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;

ll dp[1000000];
int main() {
	ll n; scanf("%lld", &n);
	dp[0] = n;
	ll sum = n - 1;
	for (int i = 1; i < n; i++) {
		dp[i] = ((n - 1)*(n - 1) + dp[i - 1] + sum) % MOD;
		sum = (sum + (i - 2 >= 0 ? dp[i - 2] : 1) + MOD - (i - n > 0 ? dp[i - n - 1] : 1)) % MOD;
	}
	printf("%lld\n", dp[n - 1]);
}