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
# dp[i] := i 項目以降を見たときの場合の数
#       = dp[i+1] + (Σ_{3<=d<=N-1} dp[i+d]) + (n-1)**2

# i 項目と i+1 項目について、
#   (1) i 項目が 1 の場合
#   (2) i 項目が 1 で無く、i+1 項目が 1 の場合
#   (3) i 項目も i+1 項目も 1 で無い場合
# で場合分けしてそれぞれを足している
# これを累積和で高速化する

# 初期化がややこしい

N = int(input())
mod = 10**9+7
dp = [N] * (N+1)
dp[N-1] = N
dp[N-2] = N*N
c = N * (N+1) + N-1
const = (N-1)**2
for i in range(N-3, -1, -1):
    ans = c - dp[i+2] + const
    dp[i] = ans
    c = (c + ans - 1) % mod
print(dp[0]%mod)
