Magic Forest
题意翻译
### 题目大意
给定一个正整数$n$ ,求满足如下条件的三元组$(a,b,c)$ 的个数:
- $1 \le a \le b \le c \le n$
- $a \space xor \space b \space xor \space c=0$
- 存在一个边长分别为$a,b,c$ 的三角形。
### 输入格式
一行一个正整数$n(1 \le n \le 2500)$
### 输出格式
输出满足题意的三元组个数。
感谢U3144 浮尘ii 提供的翻译
题目描述
Imp is in a magic forest, where xorangles grow (wut?)
![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922B/eea79d64d5bc09a90f356e81b9be908191dfc1cd.png)A xorangle of order $ n $ is such a non-degenerate triangle, that lengths of its sides are integers not exceeding $ n $ , and the xor-sum of the lengths is equal to zero. Imp has to count the number of distinct xorangles of order $ n $ to get out of the forest.
Formally, for a given integer $ n $ you have to find the number of such triples $ (a,b,c) $ , that:
- $ 1<=a<=b<=c<=n $ ;
- ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922B/e65927e7d4505d57752956035449f810615b89fe.png), where ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922B/7f1c9cbc3c887d7630734a437576c704fecc514a.png) denotes the [bitwise xor](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of integers $ x $ and $ y $ .
- $ (a,b,c) $ form a non-degenerate (with strictly positive area) triangle.
输入输出格式
输入格式
The only line contains a single integer $ n $ $ (1<=n<=2500) $ .
输出格式
Print the number of xorangles of order $ n $ .
输入输出样例
输入样例 #1
6
输出样例 #1
1
输入样例 #2
10
输出样例 #2
2
说明
The only xorangle in the first sample is $ (3,5,6) $ .