Bytecomputer

You are given a sequence of $n$ integers $x_1, x_2, \dots, x_n$, each of them from the set $\{-1, 0, 1\}$. The bytecomputer is a device that allows one operation on the sequence: choose an index $i$ with $1 \le i < n$ and increase $x_{i+1}$ by $x_i$. The range of integers the bytecomputer can store is unlimited, so in principle each $x_i$ can become arbitrarily small or arbitrarily large.

You want the sequence to be non-decreasing, that is, $x_1 \le x_2 \le \dots \le x_n$. Find the minimum number of operations needed.

The first line contains one integer $n$, the length of the sequence ($1 \le n \le 1\,000\,000$).

The second line contains the $n$ elements of the sequence $x_1, x_2, \dots, x_n$ in order, separated by single spaces ($x_i \in \{-1, 0, 1\}$).

Print on one line the minimum number of operations that make the sequence non-decreasing. If no sequence of operations achieves that, print BRAK instead. BRAK is Polish for none.

Three operations turn the sequence $-1, 1, 0, -1, 0, 1$ into $-1, -1, -1, -1, 0, 1$.