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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
long long ans=1,sum=0,b,d[310][100010],p[310]={1};
int main(){
  int n,s=0,i,j,k,M=998244353,a[310];
  d[0][0]=1;
  for(i=0;i<300;i++)p[i+1]=(p[i]*2)%M;
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&a[i]);
    s+=a[i];
  }
  for(i=0;i<n;i++)ans=(ans*3)%M;
  for(i=0;i<n;i++){
    for(j=i+1;j--;){
      for(k=s;k--;)d[j+1][k+a[i]]=(d[j][k]+d[j+1][k+a[i]])%M;
    }
  }
  /*for(i=0;i<=n;i++){
    for(j=0;j<=s;j++)printf("%lld ",d[i][j]);
    printf("\n");
    }//*/
  //printf("%d\n",s);
  for(i=(s+1)/2;i<=s;i++){
    for(j=0;j<=n;j++){
      b=p[n-j];
      if(i*2==s)b--;
      sum=(sum+d[j][i]*b)%M;
    }
  }
  sum=sum*3%M;
  printf("%lld\n",(ans-sum+M)%M);
  return 0;
}