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 <iostream>
#include <cstdio>

const int MAXN = 1e6;
const int MOD = 1e9 + 7;

int n, sum;
int dp[MAXN + 2];

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