使用C++完成此题，语言标准C++11，给出完整，正确的代码。1s/512M.

题目描述

We are given an array $a_0, a1, \cdots, a{2^n - 1} of length 2^n. For a string q of length n over the alphabet 0,1,? (1-indexed), define the "generalized subset sum" S(q) as the sum of a_j over all indices j$ that satisfy:

• For each 1 \le k \le n, if q_k = 0 then the k-th bit of j is 0.
• For each 1 \le k \le n, if q_k = 1 then the k-th bit of j is 1.
• If q_k = ? there is no restriction on the k-th bit of j.

For example, when n = 3 and s = 0?1, the generalized subset sum is S(q) = a_4 + a_6 (binary 100 and 110). Note that the first bit is the lowest bit.

Your task is to compute the generalized subset sum for each string of length n over the alphabet 0,1,?. Because the total output can be large, you only need to output the bitwise XOR of all these sums.

输入格式

The first line of the input contains an integer n (1 \le n \le 16).

The second line of the input contains 2^n integers $a_0, a1, \cdots, a{2^n} (0 \le a_i \le 9), contents in array a$.

输出格式

Print an integer denoting the bitwise-XOR of all generalized subset sums.

输入输出样例 #1

输入 #1

1
3 5

输出 #1

14

输入输出样例 #2

输入 #2

2
2 6 8 8

输出 #2

0

说明/提示

The following are query strings q and their corresponding generalized subset sums S(q) in sample 2:

q = 00, S(q) = a_0 = 2

q = 10, S(q) = a_1 = 6

q = ?0, S(q) = a_0 + a_1 = 2 + 6 = 8

q = 01, S(q) = a_2 = 8

q = 11, S(q) = a_3 = 8

q = ?1, S(q) = a_2 + a_3 = 16

q = 0?, S(q) = a_0 + a_2 = 10

q = 1?, S(q) = a_1 + a_3 = 14

q = ??, S(q) = a_0 + a_1 + a_2 + a_3 = 24

Now it is easy to verify that the output is 0.