CF1152D.Neko and Aki's Prank

Neko is playing with his toys on the backyard of Aki's house. Aki decided to play a prank on him, by secretly putting catnip into Neko's toys. Unfortunately, he went overboard and put an entire bag of catnip into the toys...

It took Neko an entire day to turn back to normal. Neko reported to Aki that he saw a lot of weird things, including a trie of all correct bracket sequences of length $2n$.

The definition of correct bracket sequence is as follows:

• The empty sequence is a correct bracket sequence,
• If $s$ is a correct bracket sequence, then $(\,s\,)$ is a correct bracket sequence,
• If $s$ and $t$ are a correct bracket sequence, then $st$ is also a correct bracket sequence.

For example, the strings "(())", "()()" form a correct bracket sequence, while ")(" and "((" not.

Aki then came up with an interesting problem: What is the size of the maximum matching (the largest set of edges such that there are no two edges with a common vertex) in this trie? Since the answer can be quite large, print it modulo $10^9 + 7$.

Neko 正在 Aki 家的后院玩他的玩具。Aki 决定捉弄他一下，偷偷把猫薄荷放进了 Neko 的玩具里。不幸的是，他玩过头了，竟把整整一袋猫薄荷都倒进了玩具中……

Neko 花了一整天才恢复正常。Neko 向 Aki 报告说，他看到了许多奇怪的东西，其中包括一棵由所有长度为 $2n$ 的合法括号序列构成的 字典树（trie）。

合法括号序列的定义如下：

• 空序列是一个合法括号序列；
• 若 $s$ 是一个合法括号序列，则 $(\,s\,)$ 也是一个合法括号序列；
• 若 $s$ 和 $t$ 都是合法括号序列，则 $st$（即 $s$ 与 $t$ 的连接）也是一个合法括号序列。

例如，字符串 "(())" 和 "()()" 是合法括号序列，而 ")(" 和 "((" 则不是。

随后，Aki 想出了一个有趣的问题：这棵 trie 中最大匹配（即边数最多的匹配，其中任意两条边不共享顶点）的大小是多少？由于答案可能非常大，请将结果对 $10^9 + 7$ 取模后输出。

The only line contains a single integer $n$ ($1 \le n \le 1000$).

唯一的一行包含一个整数 $n$（$1 \le n \le 1000$）。

Print exactly one integer — the size of the maximum matching in the trie. Since the answer can be quite large, print it modulo $10^9 + 7$.

输出一个整数——字典树中最大匹配的大小。由于答案可能非常大，请对 $10^9 + 7$ 取模后输出。

The pictures below illustrate tries in the first two examples (for clarity, the round brackets are replaced with angle brackets). The maximum matching is highlighted with blue.

下面的图片展示了前两个例子中的字典树（为清晰起见，圆括号被替换为尖括号）。最大匹配以蓝色高亮显示。