The function is given a string consisting of digits. Create a function that generates a set of all possible valid IP-addresses using all digits. The address has four groups. Each group is a number from 0 to 255 inclusive; the number cannot have leading zeros unless it equals zero.

For example, "0.1.2.201" and "192.168.1.1" are valid IP addresses while "3.011.255.245" and "192.168.1.312" are invalid IP addresses. If no single address can be produced, return an empty set.

Examples

generate_ip_addresses("0101203") ➞ {"0.101.20.3", "0.10.120.3", "0.10.1.203"}

generate_ip_addresses("25525511135") ➞ {"255.255.11.135", "255.255.111.35"}

generate_ip_addresses("0000") ➞ {"0.0.0.0"}

generate_ip_addresses("010010") ➞ {"0.10.0.10", "0.100.1.0"}

Notes

N/A