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 <iostream>

using namespace std;

constexpr int N = 1000001, mod = 1000000007;

int64_t da[N], ans = 1, cv = 1;

int64_t prod(int64_t a, int64_t b) {return a * b % mod;}
int64_t mul(int64_t &a, int64_t b) {return (a *= b) %= mod;}
int64_t add(int64_t &a, int64_t b) {return (a += b) %= mod;}

int main()
{
    int n;
    cin >> n;
    for (int i = 1; i <= n; ++i)
        add(da[i + 3], add(cv, add(da[i], da[i - 1]))),
        add(ans, prod(cv, prod(n - 1, i == n? 1: n)));
    cout << ans << '\n';
    return 0;
}