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;

const ll mod = 1e9 + 7;

ll S1[1010101], S2[1010101];
ll n, ans;

int main()
{
	ll i, x;
	
	scanf("%lld", &n);
	
	ans = 1;
	
	for(i=0; i<n; i++){
		if(i >= 3) x = ((i - 2) * S1[i - 3] - S2[i - 3] + mod + 1) % mod;
		else x = 1;
		
		if(i < n) ans = (ans + x * (n - 1)) % mod;
		if(i < n - 1) ans = (ans + x * (n - 1) % mod * (n - 1)) % mod;
		
		S1[i] = (S1[i - 1] + x) % mod;
		S2[i] = (S2[i - 1] + x * i) % mod;
	}
	
	printf("%lld\n", ans);
	
	return 0;
}