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 Julia (0.5.0) (judge verdict: Runtime Error)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
	q = 998244353
	n = readline() |> parseInt
	a = zeros(Int,n)
	for i in 1:n
		a[i] = readline() |> parseInt
	end
	s = sum(a)
	dp = zeros(Int,n+1,s+1,n+1)
	dp[1,1,1] = 1
	for i in 1:n
		for j in 1:s+1
			for k in 1:n
				if dp[i,j,k]>0
					dp[i+1,j,k] += dp[i,j,k]
					dp[i+1,j+a[i],k+1] += dp[i,j,k]
				end
			end
		end
	end
	x = 0
	k2 = zeros(Int32,n+1)
	k2[1] = 1
	for i in 2:n+1
		k2[i] = (k2[i-1]*2)%q
	end
	for j in (s+1)>>1+1:s+1
		for k in 1:n-2
			if dp[n+1,j,k+1] > 0
				x = (((k2[n-k+1]-2)*3*dp[n+1,j,k+1]%q)+x)%q
			end
		end
	end
	y = 1
	for i in 1:n
		y = (y*3)%q
	end
	z = y-3*k2[n+1]-x+3
	while z<0
		z += q
	end
	println(z)
end

main()