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B - Balance

Score : $200$ points

Problem Statement

We have $N$ weights indexed $1$ to $N$. The mass of the weight indexed $i$ is $W_i$.

We will divide these weights into two groups: the weights with indices not greater than $T$, and those with indices greater than $T$, for some integer $1 \leq T < N$. Let $S_1$ be the sum of the masses of the weights in the former group, and $S_2$ be the sum of the masses of the weights in the latter group.

Consider all possible such divisions and find the minimum possible absolute difference of $S_1$ and $S_2$.

Constraints

• $2 \leq N \leq 100$
• $1 \leq W_i \leq 100$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$W_1$ $W_2$ $...$ $W_{N-1}$ $W_N$

Output

Print the minimum possible absolute difference of $S_1$ and $S_2$.

3
1 2 3

0

If $T = 2$, $S_1 = 1 + 2 = 3$ and $S_2 = 3$, with the absolute difference of $0$.

4
1 3 1 1

2

If $T = 2$, $S_1 = 1 + 3 = 4$ and $S_2 = 1 + 1 = 2$, with the absolute difference of $2$. We cannot have a smaller absolute difference.

8
27 23 76 2 3 5 62 52

2