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;

const long long MOD = 1e9 + 7;
long long D[1000009], P[1000009];

int main() {
	long long N; scanf("%lld",&N);
	D[1] = N; D[2] = N*N;
	P[1] = N; P[2] = N*N+N;
	for(int i=3; i<=N; i++) {
		D[i] = D[i-1] + (N-1)*(N-1) + (i-3 >= 0 ? P[i-3] : 0) + N-i+2;
		D[i] %= MOD;
		P[i] = (P[i-1] + D[i]) % MOD;
	}
	printf("%lld", D[N]);
	return 0;
}