Problem: You are given N integers A_1, A_2, ..., A_N.

Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.

Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.

Find the median of this list, S_{2^{N-1}}.

Constraints

* 1 \leq N \leq 2000
* 1 \leq A_i \leq 2000
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the median of the sorted list of the sums of all non-empty subsequences of A.

Examples

Input

3
1 2 1


Output

2


Input

1
58


Output

58

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.Arrays;
import java.util.StringJoiner;
import java.util.StringTokenizer;
import java.util.function.Function;

public class Main {

    static int N;
    static int[] A;

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

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

    static int solve() {

        int sum = 0;
        BitSet bs = new BitSet(2000*N+1);
        for (int i = 0; i < N; i++) {
            int a = A[i];
            BitSet cs = bs.copy();
            bs.shiftL(a);
            cs.or(bs);
            cs.set(a, true);
            bs = cs;

            sum += a;
        }

        for (int i = (sum+1)/2; i < 2000*N+1; i++) {
            if( bs.get(i) ) return i;
        }
        throw new RuntimeException("wtf");
    }

    static class BitSet {

        long[] bits;

        BitSet(int size) {
            bits = new long[((size + 63) / 64)];
        }

        private BitSet(long[] bits) {
            this.bits = bits;
        }

        void set(int index, boolean bit) {
            int q = index / 64;
            int r = index % 64;
            if (bit) {
                bits[q] |= 1L << r;
            } else {
                bits[q] &= ~(1L << r);
            }
        }

        boolean get(int index) {
            int q = index / 64;
            int r = index % 64;
            return (bits[q] & (1L << r)) != 0L;
        }

        void shiftR(int n) {
            int q = n / 64;
            int r = n % 64;
            for (int i = 0; i < bits.length; i++) {
                int src = i + q;
                if (src < bits.length) {
                    bits[i] = bits[src] >>> r;
                    if (r > 0 && src + 1 < bits.length) {
                        bits[i] |= bits[src + 1] << (64 - r);
                    }
                } else {
                    bits[i] = 0L;
                }
            }
        }

        void shiftL(int n) {
            int q = n / 64;
            int r = n % 64;
            for (int i = bits.length - 1; i >= 0; i--) {
                int src = i - q;
                if (src >= 0) {
                    bits[i] = bits[src] << r;
                    if (r > 0 && src > 0) {
                        bits[i] |= bits[src - 1] >>> (64 - r);
                    }
                } else {
                    bits[i] = 0L;
                }
            }
        }

        void or(BitSet b) {
            for (int i = 0; i < bits.length; i++) {
                bits[i] |= b.bits[i];
            }
        }

        void and(BitSet b) {
            for (int i = 0; i < bits.length; i++) {
                bits[i] &= b.bits[i];
            }
        }

        BitSet copy() {
            return new BitSet(Arrays.copyOf(bits, bits.length));
        }
    }

    @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 <A> void writeLines(A[] as, Function<A, String> f) {
        PrintWriter pw = new PrintWriter(System.out);
        for (A a : as) {
            pw.println(f.apply(a));
        }
        pw.flush();
    }

    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 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 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());
    }
}