Bessie the cow has designed what she thinks will be the next big hit video game: "Angry Cows". The premise, which she believes is completely original, is that the player shoots a cow with a slingshot into a one-dimensional scene consisting of a set of hay bales located at various points on a number line; the cow lands with sufficient force to detonate the hay bales in close proximity to her landing site, which in turn might set of a chain reaction that causes additional hay bales to explode. The goal is to use a single cow to start a chain reaction that detonates all the hay bales.
There are NN hay bales located at distinct integer positions x1,x2,…,xNx1,x2,…,xN on the number line. If a cow is launched with power RR landing at position xx, this will causes a blast of "radius RR", engulfing all hay bales within the range x−R…x+Rx−R…x+R. These hay bales then themselves explode (all simultaneously), each with a blast radius of R−1R−1. Any not-yet-exploded bales caught in these blasts then all explode (all simultaneously) with blast radius R−2R−2, and so on.
Please determine the minimum amount of power RR with which a single cow may be launched so that, if it lands at an appropriate location, it will cause subsequent detonation of every single hay bale in the scene.
BZPRO