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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

N = int(input())
vals = []
for _ in range(N):
	vals.append(int(input()))

vals = sorted(vals)

total_val = sum(vals)
ans_dict_bigger={}
ans_dict_eq_2={}

def calc_bigger(i,r):
	if i == N:
		return 1 if r >=total_val/2 else 0
	
	if (i,r) in ans_dict_bigger.keys():
		return ans_dict_bigger[(i,r)]
	

	ret = calc_bigger(i+1,r+vals[i]) + 2*calc_bigger(i+1,r)
	ans_dict_bigger[(i,r)] = ret
	return ret


def calc_eq_2(i,r):
	if i == N:
		return 1 if r ==total_val/2 else 0
		
	if (i,r) in ans_dict_eq_2.keys():
		return ans_dict_eq_2[(i,r)]
	

	ret = calc_eq_2(i+1,r+vals[i]) + calc_eq_2(i+1,r)
	ans_dict_eq_2[(i,r)] = ret
	return ret

if total_val % 2 == 0:
	ptn_num = 3 ** N - 3*(calc_bigger(0,0) - calc_eq_2(0,0))
else:
	ptn_num = 3 ** N - 3*(calc_bigger(0,0))

print(ptn_num % 998244353)