Problem:
Score : 600 points

Problem Statement

You are given N integers. The i-th integer is a_i.
Find the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the following condition is satisfied:

Let R, G and B be the sums of the integers painted red, green and blue, respectively. There exists a triangle with positive area whose sides have lengths R, G and B.

Constraints

3 \leq N \leq 300

1 \leq a_i \leq 300(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_N

Output

Print the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the condition is satisfied.

Sample Input 1

4
1
1
1
2

Sample Output 1

18

We can only paint the integers so that the lengths of the sides of the triangle will be 1, 2 and 2, and there are 18 such ways.

Sample Input 2

6
1
3
2
3
5
2

Sample Output 2

150

Sample Input 3

20
3
1
4
1
5
9
2
6
5
3
5
8
9
7
9
3
2
3
8
4

Sample Output 3

563038556

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        Modulo m = new Modulo(MiscUtils.MODF);

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int[] a = in.readIntArray(n);

            long[] dp = new long[100000];
            long[] dp2 = new long[100000];
            dp[0] = 1;
            dp2[0] = 1;
            int sum = 0;
            for (int i = 0; i < n; i++) {
                for (int j = dp.length - 1; j >= 0; j--) {
                    dp[j] = m.mlt(dp[j], 2);
                    if (j - a[i] >= 0) {
                        dp[j] = m.add(dp[j], dp[j - a[i]]);
                        dp2[j] = m.add(dp2[j], dp2[j - a[i]]);
                    }
                }
                sum += a[i];
            }

            long ans = m.pow(3, n);
            for (int i = sum / 2 + 1; i <= sum; i++) {
                ans = m.sub(ans, dp[i] * 3);
            }
            if (sum % 2 == 0) {
                ans = m.sub(ans, dp[sum / 2] * 3);
                ans = m.add(ans, dp2[sum / 2] * 3);
            }

            out.printLine(ans);
        }

    }

    static class Modulo {
        long m;

        public Modulo(long m) {
            this.m = m;
        }

        public long add(long a, long b) {
            return (a + b) % m;
        }

        public long sub(long a, long b) {
            return (a - b + m) % m;
        }

        public long mlt(long a, long b) {
            return (a * b) % m;
        }

        public long pow(long a, long x) {
            long ans = 1 % m;
            while (x > 0) {
                if ((x & 1) != 0) {
                    ans = (ans * a) % m;
                }
                x >>= 1;
                a = (a * a) % m;
            }
            return ans;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = readInt();
            }
            return array;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class MiscUtils {
        public static final int MODF = 998244353;

    }
}