Problem:
Score : 1000 points

Problem Statement

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.

Sample Input 1

2

Sample Output 1

4

The four sequences that satisfy the conditions are:

1, 1, 1, ...

1, 2, 2, ...

2, 1, 1, ...

2, 2, 2, ...

Sample Input 2

654321

Sample Output 2

968545283

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

#define fi first
#define se second
#define mp make_pair
#define pb push_back

using namespace std;
typedef long long ll;

const int maxn = 1e6 + 5, base = 1e9 + 7;

int f[maxn];
int n;

signed main(void)
{
  ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
  cin >> n;
  f[0] = 0;
  f[1] = n;
  f[2] = 1ll * n * n % base;
  int sum = 0;
  for (int i = 3; i <= n; i++) {
    f[i] = (f[i - 1] + 1ll * (n - 1) * (n - 1) % base) % base;
    f[i] = (f[i] + sum + n - i + 2) % base;
    sum = (sum + f[i - 2]) % base;
  }
  cout << f[n] << '\n';
}