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;

int main(){
    constexpr unsigned long MOD = 1000000007;
    unsigned long N;
    cin >> N;
    unsigned long dp{N};
    vector<unsigned long> sum(N + 3, (N - 1) * N % MOD);
    sum[3] = (N * N - 1) % MOD;
    for(unsigned long i = 4; i != N + 3; ++i)sum[i] = (sum[i - 1] - 1 + ((dp += sum[i - 3]) %= MOD)) % MOD;
    cout << dp << endl;
    return 0;
}