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>
#include <cstring>
#include <iostream>
using namespace std;

typedef long long ll;
const int MAXN = 1100000;
const int MOD = 1e9 + 7;
ll dp[MAXN], sumv;

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