You are given a binary array possible of length n.

Alice and Bob are playing a game consisting of n levels in order. Each level i is represented by possible[i]:

• If possible[i] == 1, the player who plays level i gains $1$ point.

• If possible[i] == 0, the player who plays level i loses $1$ point.

Alice plays first and completes a prefix of the levels. Bob then plays the remaining levels to the end. Both Alice and Bob must play at least $1$ level.

Return the minimum number of levels Alice must play to earn strictly more total points than Bob. If it is impossible for Alice to obtain more points than Bob, return $-1$.

Constraints:

• $2 \leq n =$ possible.length $\leq 10^5$

• possible[i] is either $0$ or $1$.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.