Ilya and Matrix

题意翻译

给一个 $m\times m$ 的矩阵 $a$，$m$ 为 $2^i$（$i\in Z$）,设它的美丽值为矩阵最大元素值加四个 $\frac m 2\times \frac m 2$ 的矩阵的美丽值之和（无法分拆则结束递归），给定 $m\times m$ 的值以及每个元素的值，求能取到的最大美丽值。

题目描述

Ilya is a very good-natured lion. He likes maths. Of all mathematical objects, his favourite one is matrices. Now he's faced a complicated matrix problem he needs to solve. He's got a square $ 2^{n}×2^{n} $ -sized matrix and $ 4^{n} $ integers. You need to arrange all these numbers in the matrix (put each number in a single individual cell) so that the beauty of the resulting matrix with numbers is maximum. The beauty of a $ 2^{n}×2^{n} $ -sized matrix is an integer, obtained by the following algorithm: 1. Find the maximum element in the matrix. Let's denote it as $ m $ . 2. If $ n=0 $ , then the beauty of the matrix equals $ m $ . Otherwise, a matrix can be split into 4 non-intersecting $ 2^{n-1}×2^{n-1} $ -sized submatrices, then the beauty of the matrix equals the sum of number $ m $ and other four beauties of the described submatrices. As you can see, the algorithm is recursive. Help Ilya, solve the problem and print the resulting maximum beauty of the matrix.

输入输出格式

输入格式

The first line contains integer $ 4^{n} $ $ (1<=4^{n}<=2·10^{6}) $ . The next line contains $ 4^{n} $ integers $ a_{i} $ $ (1<=a_{i}<=10^{9}) $ — the numbers you need to arrange in the $ 2^{n}×2^{n} $ -sized matrix.

输出格式

On a single line print the maximum value of the beauty of the described matrix. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

输入输出样例

输入样例 #1

1
13

输出样例 #1

13

输入样例 #2

4
1 2 3 4

输出样例 #2

14

说明

Consider the second sample. You need to arrange the numbers in the matrix as follows: `<br></br>1 2<br></br>3 4<br></br>`Then the beauty of the matrix will equal: 4 + 1 + 2 + 3 + 4 = 14.