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
import sys
input = sys.stdin.readline

MOD = 10**9 + 7
N = int(input())

dp = [0] * (N+10)
dp_cum = [0] * (N+10)

dp[1] = N-1; dp_cum[1] = N-1
dp[2] = N-1; dp_cum[2] = 2*(N-1)
for n in range(3,N+1):
    dp[n] = dp[n-1] + dp_cum[n-3]
    dp_cum[n] = (dp_cum[n-1] + dp[n]) % MOD

answer = sum(dp[1:N])*N + dp[N] + 1
answer %= MOD
print(answer)