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 (1000010)
#define mod (1000000007)
#define ll long long

int n;
ll dp[MAXN], sum;

int main(){
	scanf("%d", &n);
	dp[1] = n;
	dp[2] = (dp[1] + (1ll) * (n - 1) * (n - 1) + (n - 1)) % mod;
	sum = dp[1] + dp[2];
	for(int i = 3; i <= n; ++ i){
		dp[i] = ((sum - dp[i - 2] + (1ll) * (n - 1) * (n - 1) + (n - i + 2)) % mod + mod) % mod;
		sum = (sum + dp[i]) % mod;
	}
	printf("%lld\n", dp[n]);
	return 0;
}