Switch

You are walking past a row of $K$ lights ($4 \le K \le 25$). Each light is either on or off. In the initial configuration there is no run of four or more consecutive lights that are all on.

The lights follow one rule: whenever four or more consecutive lights are on at the same time, that entire block of consecutive lit lights immediately turns off.

You may only switch a light from off to on (you can never turn a light off yourself). Turning on one light counts as a single action, and the automatic turn-off above may trigger right after any action.

Determine the minimum number of lights you must turn on so that, in the end, all $K$ lights are off.

The first line contains the integer $K$, the number of lights.

Each of the next $K$ lines contains a single integer: $0$ if that light is off, or $1$ if that light is on. The lights are given in row order.

Print a single integer: the minimum number of lights you must turn on so that all $K$ lights end up off.