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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
  "bufio"
  "os"
  "strconv"
  "strings"
  "fmt"
)

var reader = bufio.NewReaderSize(os.Stdin, 1000000)
var writer = bufio.NewWriter(os.Stdout)
func NextLine() string {
  buffer := make([]byte, 0)
  for true {
    line, isPrefix, err := reader.ReadLine()
    if err != nil { panic(err) }
    buffer = append(buffer, line...)
    if !isPrefix { break }
  }
  return string(buffer)
}
func NextInt() int {
  n, _ := strconv.Atoi(NextLine())
  return n
}
func NextIntVec() []int {
  L := strings.Split(NextLine(), " ")
  N := make([]int, len(L))
  for i := range N {
    N[i], _ = strconv.Atoi(L[i])
  }
  return N
}
func Write(s interface{}) {
  fmt.Fprintln(writer, s)
}
func Output() {
  _ = writer.Flush()
}

func MinInt(A ...int) int {
  min := A[0]
  for _, a := range A {
    if a < min { min = a }
  }
  return min
}
func SumInt(A ...int) int {
  sum := 0
  for _, a := range A {
    sum += a
  }
  return sum
}

const p = 998244353

func Solve() {
  N := NextInt()
  A := make([]int, N)
  for i := range A {
    A[i] = NextInt()
  }
  S := SumInt(A...)
  L := S / 2 + 1
  DP := make([][]int, N + 1)
  for i := range DP {
    DP[i] = make([]int, L + 1)
  }
  DP[0][0] = 1
  for i, a := range A {
    for j := range DP[i] {
      DP[i + 1][j] += 2 * DP[i][j]
      DP[i + 1][j] %= p
      DP[i + 1][MinInt(j + a, L)] += DP[i][j]
      DP[i + 1][MinInt(j + a, L)] %= p
    }
  }
  P := 1
  for i := 0; i < N; i++ {
    P = P * 3 % p
  }
  ans := (P + p - 3 * DP[N][L]) % p
  if S % 2 < 1 { ans = (ans + p - DP[N][S / 2] * 8 / 3) % p}
  Write(ans)
  return
}

func main() {
  Solve()
  Output()
}