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)
    exit()

dp = [0] * (n)
dp[0] = 1
dp[1] = 1
dpsum = 2
for l in range(2, n):
    dp[l] = dpsum
    dp[l] -= dp[l-2]
    dp[l] %= MOD
    dpsum += dp[l]
    dpsum %= MOD

ans = 1 + (dpsum - dp[-1]) * (n-1) # end with "1..."
ans %= MOD
for l in range(n-1):
    ans += dp[l] * (n - 1) ** 2
    ans %= MOD

ans += dp[n-1] * (n - 1)
ans %= MOD

print(ans)