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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

#define MOD (1000000007L)



int main(void)
{
    long n;
    scanf("%ld",&n);

    long P1 = 1;
    long P2 = 1;
    long P3 = 2;

    if (n == 1) {
        printf("1\n");
    } else if (n == 2){
        printf("4\n");
    } else {
        for (long i = 3; i < n; i++) {
            const long newP = (P3 + (P3 -  (P2 - P1))%MOD) % MOD;
            P1 = P2;
            P2 = P3;
            P3 = newP;
        }
        printf("%ld\n", (1L + ((n-1L)%MOD) * ((n * (P3 - (P2 - P1)))%MOD + P2)%MOD + MOD)%MOD);
    }

    return 0;
}