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
MOD = 10**9 + 7
n = int(input())
if n == 1:
	print(1)
else:
	dp = [0 for _ in range(n+1)]
	dp[0], dp[1], dp[2] = 1, 1, 1
	cum = [0 for _ in range(n+1)]
	cum[0], cum[1], cum[2] = 1, 2, 3
	for i in range(3, n+1):
		dp[i] = (dp[i-1] + cum[i-3]) % MOD
		cum[i] = (cum[i-1] + dp[i]) % MOD
	ans = cum[n-2] * (n-1) * (n-1) + dp[n-1] * (n-1) + cum[n-2] * (n-1) + 1
	print(ans%MOD)