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;

typedef long long LL;
const LL mod = 1e9+7;
LL dp[1000003];
int main()
{
    LL n, sum=0;
    scanf("%lld",&n);
    dp[1] = n;
    dp[2] = (n*n)%mod;
    for(int i=3; i<=n; ++i)
    {
        sum = (sum + dp[i-3])%mod;
        dp[i] = (dp[i-1] + sum + (n-1)*(n-1)%mod + n-i+2)%mod;
    }
    printf("%lld\n",dp[n]);
    return 0;
}
