SQL: I have a table with multiple identifiers. If any one identifier matches, I want it to roll up to the same master identifier

Question

I have a table of unique identifier combinations that belong to the same person. Sometimes, a person can sometimes have multiple phone numbers and multiple emails. I would like to add a third column to the table that is a personid. If either the phone or the email matches the phone or email in another row, those rows should have the same personid. To give an example, if this is the table.

Phone	Email
800000000	hello
777777777	unique
800000000	hi
555555555	hi

This is the desired output.

Phone	Email	PersonID
800000000	hello	1
777777777	unique	2
800000000	hi	1
555555555	hi	1

If it was a one to many relationship, I would just use rank to give each phone or email a corresponding number. However, that only works one direction. I tried to give each column a unique rank or aggregating values that should be combined into an array, but I am stuck figuring out how to use the values to get the desired output

This is what I started with.

Phone	Email
800000000	hello
777777777	unique
800000000	hi
555555555	hi

I tried to get arrays of the values that match in the other column.

Phone	Email Array
800000000	hello, hi
777777777	unique
555555555	hi

Email	Phone Array
hello	800000000
unique	777777777
hi	800000000 , 555555555

But I can't figure out how to join them together.

I am specifically using snowflake.