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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define MOD 1000000007
int32_t main() {
    int n;
    cin>>n;
    int dp[n+5];
    dp[1] = n;
    dp[2] = n*n;
    int ps = dp[1]+dp[2];
    for(int i=3; i<=n; i++){
        dp[i] = ps - dp[i-2] + ((n-1)*(n-1)) + (n-i+2);
        dp[i] %= MOD;
        if(dp[i] < 0) dp[i]+=MOD;
        ps+=dp[i];
        ps%=MOD;
        if(ps<0) ps+=MOD;
    }
    cout<<dp[n];
}