Because an integer in [0, 2/n - I] can be expressed as an n-bit binary number in a DHT, each key can be expressed as k =(k0' k1 . .. , k0_1,), and each peer idenn tifier can be expressed P =(p0' Pl' ... ,Pn-1 ,). Let's now define the XOR distance between a key k and peer P as

Describe how this metric can be used to assign (key, value) pairs to peers. (To learn about how to build an efficient DHT using this natural metric, see [Maymounkov 2002] in whjch the Kademlia DHT is described.)

d(k, p) = Ik,-P,I 2' P,1 2 ja0