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 int mod = 1e9+7;
typedef long long LL;
LL dp[1000005];
int main(){
    int n;
    scanf("%d", &n);

    LL res1 = (n-1)*1ll*n%mod;
    LL res2 = 0;
    dp[1] = n;
    for(int i=2;i<=n;i++){
        if(i >= 4){
            res1 = (res1 - n + mod)%mod;
            res2 = (res2 + dp[i-3] + n-1)%mod;
        }
        dp[i] = (dp[i-1] + res1 + res2)%mod;
    }
    printf("%lld\n", dp[n]);
}