AT_agc071_a [AGC071A] XOR Cross Over

*(In this problem statement, all sequences consist of non-negative integers.)* There is a blackboard on which sequences are written. Initially, the blackboard only has one length- $ N $ sequence $ A=(A_1,A_2,\dots,A_N) $ . We repeat the following operation until all sequences on the blackboard are of length $ 1 $ : - Among the sequences on the blackboard, choose one that has length at least $ 2 $ , and remove it from the blackboard. Let the chosen sequence be $ B=(B_1,B_2,\dots,B_n) $ . Then, choose an integer $ k $ satisfying $ 1 \leq k < n $ , and define $ X = B_1 \oplus B_2 \oplus \dots \oplus B_k $ and $ Y=B_{k+1} \oplus B_{k+2} \oplus \dots \oplus B_n $ . Finally, write two sequences $ (B_1 \oplus Y, B_2 \oplus Y,\dots,B_k \oplus Y) $ and $ (B_{k+1} \oplus X,\ B_{k+2} \oplus X,\dots,B_n \oplus X) $ on the blackboard. Here, $ \oplus $ denotes the bitwise $ \mathrm{XOR} $ operation. After this series of operations, let $ (C_1),(C_2),\dots,(C_N) $ be the $ N $ sequences of length $ 1 $ on the blackboard. Find the minimum possible value of $ \sum_{i=1}^{N} C_i $ . Notes on the bitwise $ \mathrm{XOR} $ operation For two non-negative integers $ A, B $ , the bitwise $ \mathrm{XOR} $ operation $ A \oplus B $ is defined as follows. - When $ A \oplus B $ is written in binary, for each $ 2^k $ place ( $ k \geq 0 $ ), the bit is 1 if and only if exactly one of the bits in the $ 2^k $ place of $ A $ and $ B $ (in binary) is 1, and 0 otherwise. For example, $ 3 \oplus 5 = 6 $ (in binary notation: $ 011 \oplus 101 = 110 $ ). In general, the bitwise $ \mathrm{XOR} $ of $ k $ non-negative integers $ p_1, p_2, p_3, \dots, p_k $ is defined as $ (\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k) $ , and it can be proved that this value does not depend on the order of $ p_1, p_2, \dots, p_k $ .

The input is given from Standard Input in the following format: > $ N $ $ A_1 $ $ A_2 $ $ \dots $ $ A_N $

Print the answer.

### Sample Explanation 1 Initially, the blackboard has $ (1,3,4,5) $ written on it. From here, we perform operations in the following steps. 1. Remove $ (1,3,4,5) $ from the blackboard and set $ k=2 $ . Then, $ X=1 \oplus 3=2 $ and $ Y=4 \oplus 5=1 $ , and two new sequences $ (1 \oplus 1, 3 \oplus 1)=(0,2) $ and $ (4 \oplus 2, 5 \oplus 2)=(6,7) $ are written on the blackboard. 2. Remove $ (0,2) $ from the blackboard and set $ k=1 $ . Two new sequences $ (2),(2) $ are written on the blackboard. 3. Remove $ (6,7) $ from the blackboard and set $ k=1 $ . Two new sequences $ (1),(1) $ are written on the blackboard. After these steps, the four sequences on the blackboard are $ (2),(2),(1),(1) $ , each of length $ 1 $ . Their sum is $ 2+2+1+1=6 $ . ### Constraints - $ 1 \leq N \leq 500 $ - $ 0 \leq A_i < 2^{40} $ - All input values are integers.