Alex is administrator of IP networks. His clients have a bunch of individual IP addresses and he decidedto group all those IP addresses into the smallest possible IP network.
Each IP address is a 4-byte number that is written byte-by-byte in a decimal dot-separated notation "byte0.byte1.byte2.byte3" (quotes are added for clarity). Each byte is written as a decimal number from0 to 255 (inclusive) without extra leading zeroes.
IP network is described by two 4-byte numbers - network address and network mask. Both networkaddress and network mask are written in the same notation as IP addresses.
In order to understand the meaning of network address and network mask you have to consider their binary representation. Binary representation of IP address, network address, and network mask consists of 32 bits: 8 bits for byte0 (most significant to least significant), followed by 8 bits for byte1, followed by 8 bits for byte2, and followed by 8 bits for byte3.
IP network contains a range of 2n IP addresses where 0 <= n <= 32. Network mask always has 32-n first bits set to one, and n last bits set to zero in its binary representation. Network address has arbitrary 32 - n first bits, and n last bits set to zero in its binary representation. IP network contains all IP addresses whose 32-n first bits are equal to 32-n first bits of network address with arbitrary n lastbits. We say that one IP network is smaller than the other IP network if it contains fewer IP addresses.
For example, IP network with network address 194.85.160.176 and network mask 255.255.255.248 contains 8 IP addresses from 194.85.160.176 to 194.85.160.183 (inclusive).