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())

X = [1, 1, 1]
Y = [1, 2, 3]
for i in range(3, N+2):
    x = (X[-1] + Y[i-3]) % mod
    X.append(x)
    Y.append((Y[-1]+x)%mod)

ans = ((Y[N-2] * (N-2) + (Y[N-1])) * (N-1) + (N-1) * Y[N-2] + 1) % mod
print(ans)


# from itertools import product

# A = product(range(1, N+1), repeat=N)
# P = []
# for B in A:
#     ok = True
#     B = list(B) + [B[-1]]*(N+1)
#     for i in range(N):
#         b = B[i]
#         if len(set(B[i+1:i+1+b])) != 1:
#             ok = False
#             break
#     if ok:
#         P.append(B)
# print(len(P))
# for B in P:
#     print(B)