Problem:
Score : 1000 points

Problem Statement

There is a stack of N cards, each of which has a non-negative integer written on it. The integer written on the i-th card from the top is A_i.

Snuke will repeat the following operation until two cards remain:

Choose three consecutive cards from the stack.

Eat the middle card of the three.

For each of the other two cards, replace the integer written on it by the sum of that integer and the integer written on the card eaten.

Return the two cards to the original position in the stack, without swapping them.

Find the minimum possible sum of the integers written on the last two cards remaining.

Constraints

2 \leq N \leq 18

0 \leq A_i \leq 10^9 (1\leq i\leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible sum of the integers written on the last two cards remaining.

Sample Input 1

4
3 1 4 2

Sample Output 1

16

We can minimize the sum of the integers written on the last two cards remaining by doing as follows:

Initially, the integers written on the cards are 3, 1, 4, and 2 from top to bottom.

Choose the first, second, and third card from the top. Eat the second card with 1 written on it, add 1 to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now 4, 5, and 2 from top to bottom.

Choose the first, second, and third card from the top. Eat the second card with 5 written on it, add 5 to each of the other two cards, and return them to the original position in the stack. The integers written on the cards are now 9 and 7 from top to bottom.

The sum of the integers written on the last two cards remaining is 16.

Sample Input 2

6
5 2 4 1 6 9

Sample Output 2

51

Sample Input 3

10
3 1 4 1 5 9 2 6 5 3

Sample Output 3

115

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.*;
import java.util.Arrays;
import java.util.StringJoiner;
import java.util.StringTokenizer;

public class Main {

    static int N;
    static long[] A;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        A = sc.nextLongArray(N);

        System.out.println(solve());
    }

    static long solve() {
        return dfs(A);
    }

    static long dfs(long[] curr) {
        int n = curr.length;
        if( n == 3 ) {
            long sum = 0;
            for (long v : curr) {
                sum += v;
            }
            sum += curr[1];
            return sum;

        } else {
            long min = Long.MAX_VALUE;
            long[] next = new long[curr.length-1];
            // 両端(+-1)はとりあえず食ってみる
            mkNext(1, curr, next);
            min = Math.min(min, dfs(next));
            mkNext(n-2, curr, next);
            min = Math.min(min, dfs(next));

            // 両端以外は左右で比較してよさそうな側だけ試す
            for (int i = 2; i <= n-3; i++) {
                if( curr[i] < curr[i-1] && curr[i] <= curr[i+1] ) {
                    mkNext(i, curr, next);
                    min = Math.min(min, dfs(next));
                }
            }
            return min;
        }
    }

    static void mkNext(int idx, long[] curr, long[] next) {
        for (int i = 0; i < idx; i++) {
            next[i] = curr[i];
        }
        for (int i = idx+1; i < curr.length; i++) {
            next[i-1] = curr[i];
        }
        next[idx-1] += curr[idx];
        next[idx] += curr[idx];
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static void writeSingleLine(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < as.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(as[i]);
        }
        pw.println();
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg == null) j.add("null");
            else if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }

    static void printSingleLine(int[] array) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < array.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(array[i]);
        }
        pw.println();
        pw.flush();
    }

    static int lowerBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] < value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }

    static int upperBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] <= value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }
}