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>

using namespace std;

typedef long long ll;

ll MOD = 1000000007;
ll s[1005999];

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