The social network code-golf

On my social network, two users are "friends" if their name share a common letter. For exemple, bob and bill are friends, as they share the letter b.

Given a list of user names:

• display a falsy value if there exist in the list two distinct users x and y that cannot be related through a friendship chain;
• else, display a truthy value.

Examples

abc cde efg ghi should return true, as abc is friend with cde, which is friend with efg, which is friend with ghi : all users are related.

abc cde fgh hij should return false, as for example abc and fgh cannot be related through a friendship chain.

abc should return true, as we cannot find in that list two unrelated users.

Input

• You can read the name list in any convenient format for your language.
• You can assume all the names are lowercase and use only the characters a-za-z.
• You don't need to handle the empty list, any result (true, false, program crash) is acceptable for it.